Upload original Matlab程序设计 course files (part 5)

matlab数学建模算法/MATLAB语言常用算法程序集/第4章 插值/ThrSample2.m

@@ -1,3 +1,51 @@
-version https://git-lfs.github.com/spec/v1
-oid sha256:d28d6aa66649955368e3b7c92223bcff0a32f3bb95f36f1d9f413cc5cee38488
-size 1466
+function [f,f0] = ThrSample2 (x,y,y2_1, y2_N,x0)
+syms t;
+f = 0.0;
+f0 = 0.0;
+
+if(length(x) == length(y))
+    n = length(x);
+else
+    disp('x��y��ά������ȣ�');
+    return;
+end                  %�����
+
+for i=1:n
+    if(x(i)<=x0)&& (x(i+1)>=x0)
+        index = i;
+        break;
+    end
+end                          %�ҵ�x0��������
+
+for i=1:n
+    if(x(i)<=x0)&& (x(i+1)>=x0)
+        index = i;
+        break;
+    end
+end                          %�ҵ�x0��������
+ 
+A = diag(2*ones(1,n));       %���m��ϵ������
+A(1,2) = 1;
+A(n,n-1) = 1;
+u = zeros(n-2,1);
+lamda = zeros(n-1,1);
+c = zeros(n,1);
+for i=2:n-1
+    u(i-1) = (x(i)-x(i-1))/(x(i+1)-x(i-1));
+    lamda(i) = (x(i+1)-x(i))/(x(i+1)-x(i-1));
+    c(i) = 3*lamda(i)*(y(i)-y(i-1))/(x(i)-x(i-1))+ ...
+        3*u(i-1)*(y(i+1)-y(i))/(x(i+1)-x(i));
+    A(i, i+1) = u(i-1);
+    A(i, i-1) = lamda(i);    %�γ�ϵ����������c
+end
+c(1) = 3*(y(2)-y(1))/(x(2)-x(1))-(x(2)-x(1))*y2_1/2;
+c(n) = 3*(y(n)-y(n-1))/(x(n)-x(n-1))-(x(n)-x(n-1))*y2_N/2;
+
+m = followup(A,c);           %��׷�Ϸ���ⷽ����
+h = x(index+1) - x(index);   %x0�������䳤��
+f = y(index)*(2*(t-x(index))+h)*(t-x(index+1))^2/h/h/h + ...
+        y(index+1)*(2*(x(index+1)-t)+h)*(t-x(index))^2/h/h/h + ...
+        m(index)*(t-x(index))*(x(index+1)-t)^2/h/h - ...
+        m(index+1)*(x(index+1)-t)*(t-x(index))^2/h/h;     
+                            %x0��������IJ�ֵ����
+f0 = subs(f,'t',x0);        %x0���IJ�ֵ

matlab数学建模算法/MATLAB语言常用算法程序集/第4章 插值/ThrSample3.m

@@ -1,3 +1,57 @@
-version https://git-lfs.github.com/spec/v1
-oid sha256:6f8000d9d2a9f9aa94a9e4db120bf5b1e599329e2d8db2b631f0888acdaf7b92
-size 1573
+function [f,f0] = ThrSample3 (x,y,x0)
+syms t;
+f = 0.0;
+f0 = 0.0;
+
+if(length(x) == length(y))
+    n = length(x);
+else
+    disp('x��y��ά������ȣ�');
+    return;
+end                  %�����
+
+for i=1:n
+    if(x(i)<=x0)&& (x(i+1)>=x0)
+        index = i;
+        break;
+    end
+end                          %�ҵ�x0��������
+
+for i=1:n
+    if(x(i)<=x0)&& (x(i+1)>=x0)
+        index = i;
+        break;
+    end
+end                          %�ҵ�x0��������
+ 
+A = diag(2*ones(1,n-1));       %���m��ϵ������
+h0 = x(2)-x(1);
+h1 = x(3)�Cx(2);
+he = x(n)-x(n-1);
+A(1,2) = h0/(h0+h1);
+A(1,n-1) = 1 - A(1,2);
+A(n-1,1) = he/(h0+he);
+A(n-1,n-2) = 1 - A(n-1,1);
+
+c = zeros(n-1,1);
+c(1) = 3* A(1,n-1)*(y(2)-y(1))/h0 + 3* A(1,2)*(y(3)-y(2))/h1;
+for i=2:n-2
+    u = (x(i)-x(i-1))/(x(i+1)-x(i-1));
+    lamda = (x(i+1)-x(i))/(x(i+1)-x(i-1));
+    c(i) = 3*lamda*(y(i)-y(i-1))/(x(i)-x(i-1))+ ...
+        3*u*(y(i+1)-y(i))/(x(i+1)-x(i));
+    A(i, i+1) = u;
+    A(i, i-1) = lamda;    %�γ�ϵ����������c
+end
+c(n-1) = 3*( he*(y(2)-y(1))/h0+h0*( y(n)-y(n-1))/he)/(h0+he);
+
+m = zeros(n,1);
+[m(2:n),Q,R] = qrxq(A,c);           %��qr�ֽⷨ����ⷽ����
+m(1) = m(n);
+h = x(index+1) - x(index);   %x0�������䳤��
+f = y(index)*(2*(t-x(index))+h)*(t-x(index+1))^2/h/h/h + ...
+        y(index+1)*(2*(x(index+1)-t)+h)*(t-x(index))^2/h/h/h + ...
+        m(index)*(t-x(index))*(x(index+1)-t)^2/h/h - ...
+        m(index+1)*(x(index+1)-t)*(t-x(index))^2/h/h;     
+                            %x0��������IJ�ֵ����
+f0 = subs(f,'t',x0);        %x0���IJ�ֵ

matlab数学建模算法/MATLAB语言常用算法程序集/第5章 函数逼近/Chebyshev.m

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-version https://git-lfs.github.com/spec/v1
-oid sha256:744983abe28e924f1fc5e40ec8e77e7d05c4bb349e164ad76bcccfe19edad289
-size 575
+function f = Chebyshev(y,k,x0)
+syms t;
+T(1:k+1) = t;
+T(1) = 1;
+T(2) = t;
+c(1:k+1) = 0.0;
+
+c(1)=int(subs(y,findsym(sym(y)),sym('t'))*T(1)/sqrt(1-t^2),t,-1,1)/pi;
+c(2)=2*int(subs(y,findsym(sym(y)),sym('t'))*T(2)/sqrt(1-t^2),t,-1,1)/pi;
+f = c(1)+c(2)*t;
+
+for i=3:k+1
+    T(i) = 2*t*T(i-1)-T(i-2);
+    c(i) = 2*int(subs(y,findsym(sym(y)),sym('t'))*T(i)/sqrt(1-t^2),t,-1,1)/2;
+    f = f + c(i)*T(i);
+    f = vpa(f,6);
+    
+    if(i==k+1)
+        if(nargin == 3)
+            f = subs(f,'t',x0);
+        else
+            f = vpa(f,6);
+        end
+    end
+end

matlab数学建模算法/MATLAB语言常用算法程序集/第5章 函数逼近/DFF.m

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-version https://git-lfs.github.com/spec/v1
-oid sha256:2c5220c80afc3ecd451ea7cfc689a35e4bf95833b1fc91a016d452882cd78c80
-size 136
+function c = DFF(f,N)
+c(1:N)=0;
+for(m=1:N)
+    for(n=1:N)
+        c(m)=c(m)+f(n)*exp(-i*m*n*2*pi/N);
+    end
+    c(m)=c(m)/N;
+end

matlab数学建模算法/MATLAB语言常用算法程序集/第5章 函数逼近/FZZ.m

@@ -1,3 +1,11 @@
-version https://git-lfs.github.com/spec/v1
-oid sha256:04e895cb4d427ec23fb76d6cf6d3ab98c61f59404c7e250153a42c7fbad0a7a9
-size 303
+function [A0,A,B]=FZZ(func,T, n)
+syms t;
+func = subs(sym(func), findsym(sym(func)),sym('t'));
+A0=int(sym(func),t,-T/2,T/2)/T;
+for(k=1:n)
+    A(k)=int(func*cos(2*pi*k*t/T), t,-T/2,T/2)*2/T;
+    A(k)=vpa(A(k),4);
+    B(k)=int(func*sin(2*pi*k*t/T), t,-T/2,T/2)*2/T;
+    B(k)=vpa(B(k),4);
+end
+    

matlab数学建模算法/MATLAB语言常用算法程序集/第5章 函数逼近/LZXEC.m

@@ -1,3 +1,22 @@
-version https://git-lfs.github.com/spec/v1
-oid sha256:4657e781854a873e1a3886176200f91b20bda752c6943b49a997ed1ab259e6e9
-size 408
+function [a,b]=LZXEC(x,y)
+if(length(x) == length(y))
+        n = length(x);  
+else
+    disp('x��y��ά������ȣ�');
+    return;
+end                  %�����
+
+A = zeros(2,2);
+A(2,2) = n;
+B = zeros(2,1);
+for i=1:n
+    A(1,1) = A(1,1) + x(i)*x(i);
+    A(1,2) = A(1,2) + x(i);
+    B(1,1) = B(1,1) + x(i)*y(i);
+    B(2,1) = B(2,1) + y(i);
+end
+A(2,1) = A(1,2);
+
+s = A\B;
+a = s(1);
+b = s(2);

matlab数学建模算法/MATLAB语言常用算法程序集/第5章 函数逼近/Legendre.m

@@ -1,3 +1,24 @@
-version https://git-lfs.github.com/spec/v1
-oid sha256:b58a9bba317f4b32e59a4fd8d78589e2d8116610d1694b7a9ab971b35c116b48
-size 526
+function f = Legendre(y,k,x0)
+syms t;
+P(1:k+1) = t;
+P(1) = 1;
+P(2) = t;
+c(1:k+1) = 0.0;
+
+c(1)=int(subs(y,findsym(sym(y)),sym('t'))*P(1),t,-1,1)/2;
+c(2)=int(subs(y,findsym(sym(y)),sym('t'))*P(2),t,-1,1)/2;
+f = c(1)+c(2)*t;
+
+for i=3:k+1
+    P(i) = ((2*i-3)*P(i-1)*t-(i-2)*P(i-2))/(i-1);
+    c(i) = int(subs(y,findsym(sym(y)),t)*P(i),t,-1,1)/2;
+    f = f + c(i)*P(i);
+    
+    if(i==k+1)
+        if(nargin == 3)
+            f = subs(f,'t',x0);
+        else
+            f = vpa(f,6);
+        end
+    end
+end

matlab数学建模算法/MATLAB语言常用算法程序集/第5章 函数逼近/Pade.m

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-version https://git-lfs.github.com/spec/v1
-oid sha256:8731a5f6d804a4da9b34825c7e3307cb0e4c9e31a8a889d77236377143178584
-size 780
+function f = Pade(y,n,x0)
+syms t;
+
+A = zeros(n,n);
+q = zeros(n,1);
+p = zeros(n+1,1);
+b = zeros(n,1);
+yy = 0;
+a(1:2*n) = 0.0;
+
+for(i=1:2*n)
+    yy = diff(sym(y),findsym(sym(y)),n);
+    a(i) = subs(sym(yy), findsym(sym(yy)), 0.0)/factorial(i);
+end;
+
+for(i=1:n)
+    for(j=1:n)
+        A(i,j)=a(i+j-1);
+    end;
+    b(i,1) = -a(n+i);
+end;
+
+q = A\b;
+p(1) = subs(sym(y),findsym(sym(y)),0.0);
+for(i=1:n)
+    p(i+1) = a(n)+q(i)*subs(sym(y),findsym(sym(y)),0.0);
+    for(j=2:i-1)
+        p(i+1)=p(i+1)+q(j)*a(i-j);
+    end
+end
+
+f_1 = 0;
+f_2 = 1;
+for(i=1:n+1)
+    f_1 = f_1 + p(i)*(t^(i-1));
+end
+
+for(i=1:n)
+    f_2 = f_2 + q(i)*(t^i);
+end
+
+if(nargin == 3)
+    f = f_1/f_2;
+    f = subs(f,'t',x0);
+else
+    f = f_1/f_2;
+    f = vpa(f,6);
+end

matlab数学建模算法/MATLAB语言常用算法程序集/第5章 函数逼近/SmartBJ.m

@@ -1,3 +1,64 @@
-version https://git-lfs.github.com/spec/v1
-oid sha256:84e0d55abb83831270b6bb2e75328e320f844cba1cb5b7f7739415f8cf22846b
-size 1728
+function [node,err] = SmartBJ(func,a,b,maxtol)
+format long;
+node(1) = a;
+node(2) = b;
+num = 2;
+if(b-a)<10 
+    n = 5;
+else
+    n = 10;
+end
+err = 0;
+bSign = 1;
+while (bSign)
+    bSign = 0;
+    knode = node;
+    tnum = num;
+    insert_num = 0;
+    for i=1:(tnum-1)       
+        [mx,mv] = FindMX(func,knode(i),knode(i+1),n); 
+        %�ҵ�����[knode(i),knode(i+1)]�ϵ�������ĵ�
+        if mv > maxtol   
+        %��������������ȣ��ڴ˵㽫����[knode(i),knode(i+1)]��Ϊ����
+            d(1:(i+insert_num)) = node(1:(i+insert_num));
+            d(i+insert_num+1) = mx; 
+            num = num+1;
+            d((i+insert_num+2):num) = node((i+insert_num+1):(num-1));   
+            node = d;
+            bSign = 1;  
+            insert_num = insert_num + 1;
+        else
+            if(mv>err)
+                err = mv;           %��¼���зֶ����Բ�ֵ�����ϵ�������
+            end
+        end
+    end    
+end
+format short;
+
+function [max_x,max_v] = FindMX(func,a,b,n)
+format long;
+eps = 1.e-3;
+max_v = 0; 
+max_x = a;
+fa = subs(sym(func), findsym(sym(func)),a);   %��˵㺯��ֵ
+fb = subs(sym(func), findsym(sym(func)),b);   %�Ҷ˵㺯��ֵ
+step = n/5;
+tol = 1;
+tmp = 0;
+while tol>eps
+     t = a;
+     for j=0:(n/step)       %��ѭ���ҳ�ȡ���ֵ��x
+         t = a + j*step*(b-a)/n;
+         pt = fa + (t-a)*(fb-fa)/(b-a); %���Բ�ֵ�ó��ĺ���ֵ
+         ft = subs(sym(func), findsym(sym(func)),t);
+         if abs(ft-pt)>max_v           %abs(f(x)-p(x))
+            max_v = abs(ft-pt);       %��¼������
+            max_x = t;                %��¼�˵�����
+         end
+     end   
+     tol = abs(max_x-tmp);
+     tmp = max_x;
+     step = step/2;
+end
+format short;

matlab数学建模算法/MATLAB语言常用算法程序集/第5章 函数逼近/SmartYTBJ.m

@@ -1,3 +1,70 @@
-version https://git-lfs.github.com/spec/v1
-oid sha256:f0e1c41450dff43029a5af2d65b8a716dbcd580e61ce4c8f6c6a056a9e0e3878
-size 1991
+function [node,err] = SmartYTBJ(func,a,b,y_s,y_e,maxtol)
+format long;
+node(1) = a;
+node(2) = b;
+num = 2;
+if(b-a)<10 
+    n = 5;
+else
+    n = 10;
+end
+err = 0;
+bSign = 1;
+while (bSign)
+    bSign = 0;
+    for l=1:num
+        y(l) = subs(subs(sym(func), findsym(sym(func)),node(l)));
+    end
+    knode = node;
+    tnum = num;
+    insert_num = 0;
+    for i=1:(tnum-1)
+        pfx = ThrSample1(knode,y,y_s,y_e,((knode(i)+knode(i+1))/2));
+        %��ʽ����ÿ���ֶ������ϵ�������ֵ����
+        [mx,mv] = FindMX(func,pfx,knode(i),knode(i+1),n); 
+        %�ҵ�����[knode(i),knode(i+1)]�ϵ�������ĵ�
+        if mv > maxtol   
+        %��������������ȣ��ڴ˵㽫����[knode(i),knode(i+1)]��Ϊ���Σ������˵��
+        %����������
+            d(1:(i+insert_num)) = node(1:(i+insert_num));
+            d(i+insert_num+1) = mx; 
+            num = num+1;
+            d((i+insert_num+2):num) = node((i+insert_num+1):(num-1));   
+            node = d;
+            bSign = 1;  
+            insert_num = insert_num + 1;
+        else
+            if(mv>err)
+                err = mv;           %��¼����������ֵ�����ϵ�������
+            end
+        end
+    end    
+end
+format short;
+
+function [max_x,max_v] = FindMX(func,pfx,a,b,n)
+format long;
+eps = 1.e-3;
+max_v = 0; 
+max_x = a;
+fa = subs(sym(func), findsym(sym(func)),a);   %��˵㺯��ֵ
+fb = subs(sym(func), findsym(sym(func)),b);   %�Ҷ˵㺯��ֵ
+step = n/5;
+tol = 1;
+tmp = 0;
+while tol>eps
+     t = a;
+     for j=0:(n/step)       %��ѭ���ҳ�ȡ���ֵ��x
+         t = a + j*step*(b-a)/n;
+         pt = subs(sym(pfx), findsym(sym(pfx)),t); %������ֵ�ó��ĺ���ֵ
+         ft = subs(sym(func), findsym(sym(func)),t);
+         if abs(ft-pt)>max_v           %abs(f(x)-p(x))
+            max_v = abs(ft-pt);       %��¼������
+            max_x = t;                %��¼�˵�����
+         end
+     end   
+     tol = abs(max_x-tmp);
+     tmp = max_x;
+     step = step/2;
+end
+format short;

matlab数学建模算法/MATLAB语言常用算法程序集/第5章 函数逼近/ZJPF.m

@@ -1,3 +1,17 @@
-version https://git-lfs.github.com/spec/v1
-oid sha256:5af4f34a836591f79125ed43a871bb1e3ba9d0fcde562ad9d78128fd8f8a7b60
-size 492
+function coff=ZJPF(func,n,a,b)
+C = zeros(n+1,n+1);
+var = findsym(sym(func));
+func = func/var;
+for i=1:n+1
+    C(1,i)=(power(b,i)-power(a,i))/i;       %�㷨�е�C����ĵ�һ��
+    func = func*var;
+    d(i,1)=int(sym(func),var,a,b);          %�㷨�е�D�����ĵ�һ��
+end
+
+for i=2:n+1
+    C(i,1:n)=C(i-1,2:n+1);
+    f1 = power(b,n+i);
+    f2 = power(a,n+i);
+    C(i,n+1)=(f1-f2)/(n+i);                %�γ�C���� 
+end
+coff = C\d;                                %���ƽ�����ʽ��ϵ��

matlab数学建模算法/MATLAB语言常用算法程序集/第5章 函数逼近/ZJZXEC.m

@@ -1,3 +1,61 @@
-version https://git-lfs.github.com/spec/v1
-oid sha256:b60ab187a4949ac9b4a8d8d5631feb3372f02d5d247da7542e684452570cc1fb
-size 1350
+function a=ZJZXEC(x,y,m)
+if(length(x) == length(y))
+    n = length(x);  
+else
+    disp('x��y��ά������ȣ�');
+    return;
+end                  %�����
+
+syms v;
+d = zeros(1,m+1);
+q = zeros(1,m+1);
+alpha = zeros(1,m+1);
+for k=0:m
+   px(k+1)=power(v,k);
+end                      %x���ݶ���ʽ
+B2 = [1];
+d(1) = n;
+for l=1:n
+    q(1) = q(1) + y(l);
+    alpha(1) = alpha(1) + x(l);
+end
+q(1) = q(1)/d(1);
+alpha(1) = alpha(1)/d(1);
+a(1) = q(1);
+B1 = [-alpha(1) 1];
+for l=1:n
+    d(2) = d(2) + (x(l)-alpha(1))^2;
+    q(2) = q(2) + y(l)*(x(l)-alpha(1));
+    alpha(2) = alpha(2) + x(l)*(x(l)-alpha(1))^2;
+end
+q(2) = q(2)/d(2);
+alpha(2) = alpha(2)/d(2);
+a(1) = a(1)+q(2)*(-alpha(1));
+a(2) = q(2);
+beta = d(2)/d(1);
+
+for i=3:(m+1)
+    B = zeros(1,i);
+    B(i) = B1(i-1);
+    B(i-1) = -alpha(i-1)*B1(i-1)+B1(i-2);
+    for j=2:i-2
+       B(j) = -alpha(i-1)*B1(j)+B1(j-1)-beta*B2(j);
+    end
+    B(1) = -alpha(i-1)*B1(1)-beta*B2(1);
+    BF = B*transpose(px(1:i));
+    for l=1:n
+        Qx = subs(BF,'v',x(l));
+        d(i) = d(i) + (Qx)^2;
+        q(i) = q(i) + y(l)*Qx;
+        alpha(i) = alpha(i) + x(l)*(Qx)^2;
+    end
+    alpha(i) = alpha(i)/d(i);
+    q(i) = q(i)/d(i);
+    beta = d(i)/d(i-1);
+    for k=1:i-1
+        a(k) = a(k)+q(i)*B(k);
+    end
+    a(i) = q(i)*B(i);
+    B2 = B1;
+    B1 = B;
+end

matlab数学建模算法/MATLAB语言常用算法程序集/第5章 函数逼近/lmz.m

@@ -1,3 +1,101 @@
-version https://git-lfs.github.com/spec/v1
-oid sha256:bdb73dff13de67c0feb69924fd464245701b07e9f9d6164b30710a21a7d0df9d
-size 2997
+function [coff,err]= lmz(func,m,a,b,eps) 
+if(nargin == 4)
+    eps=1.0e-6;
+end
+syms v;
+maxv = 0.0;
+max_x = a;               %��¼abs(f(x)-p(x))ȡ���ֵ��x
+for k=0:m
+   px(k+1)=power(v,k);
+end                      %p��x������ʽ
+for  i=1:m+2
+    x(i)=0.5*(a+b+(b-a)*cos(3.14159265*(m+2-i)/(m+1)));
+    fx(i)=subs(sym(func), findsym(sym(func)),x(i));
+end                      %��ʼ��x��f(x)
+A = zeros(m+2,m+2);
+for i=1:m+2
+    for j=1:m+1
+        A(i,j)=power(x(i),j-1);
+    end
+    A(i,m+2)=(-1)^i;
+end
+c =A\transpose(fx);    %p(x)�ij�ʼϵ��
+u = c(m+2);            %�㷨�е�u        
+tol = 1;               %����
+
+while(tol>eps)
+    t = a;
+    while(t<b)        %��ѭ���ҳ�abs(f(x)-p(x))ȡ���ֵ��x
+        t = t + 0.05*(b-a)/m;
+        px1 = subs(px,'v',t);
+        pt = px1*c(1:m+1);
+        ft = subs(sym(func), findsym(sym(func)),t);
+        if abs(ft-pt)>maxv
+            maxv = abs(ft-pt);
+            max_x = t;
+        end
+    end   
+    if max_x>b
+        max_x = b;
+    end   
+    %���¿ɲο��㷨������ȷ���µ㼯�����
+    if (a<=max_x)&&(max_x<=x(2))          %��һ�����
+        f0 = subs(sym(func), findsym(sym(func)),x(2));
+        px1 = subs(px,'v',x(2));
+        pt = px1*c(1:m+1);
+        d1 = f0 - pt;
+        fm = subs(sym(func), findsym(sym(func)),max_x);
+        pm1 = subs(px,'v',max_x);
+        pm = pm1*c(1:m+1);
+        d2 = fm - pm;
+        if d1*d2>0
+            x(2) = max_x;
+        end
+    else
+        if (x(m+1)<=max_x)&&(max_x<=b)   %�ڶ������
+            f0 = subs(sym(func), findsym(sym(func)),x(m+1));
+            px1 = subs(px,'v',x(m+1));
+            pt = px1*c(1:m+1);
+            d1 = f0 - pt;
+            fm = subs(sym(func), findsym(sym(func)),max_x);
+            pm1 = subs(px,'v',max_x);
+            pm = pm1*c(1:m+1);
+            d2 = fm - pm;
+            if d1*d2>0
+                x(m+1) = max_x;
+            end
+        else                           %���������
+            for i=2:m
+                if(x(i)<=max_x)&& (x(i+1)>=max_x)
+                    index_x = i;
+                    break;
+                end
+            end                       %�ҵ�max_x��������
+            f0 = subs(sym(func), findsym(sym(func)),x(index_x));
+            px1 = subs(px,'v',x(index_x));
+            pt = px1*c(1:m+1);
+            d1 = f0 - pt;
+            fm = subs(sym(func), findsym(sym(func)),max_x);
+            pm1 = subs(px,'v',max_x);
+            pm = pm1*c(1:m+1);
+            d2 = fm - pm;
+            if d1*d2>0
+                x(index_x) = max_x;
+            end
+        end
+    end
+    for  i=1:m+2                   %���¼���f��x��
+        fx(i)=subs(sym(func), findsym(sym(func)),x(i));
+    end
+    for i=1:m+2
+        for j=1:m+1
+            A(i,j)=power(x(i),j-1);
+        end
+        A(i,m+2)=(-1)^i;
+    end
+    c =A\transpose(fx);           %���¼���p��x����ϵ��
+    tol = abs(c(m+2)-u);    
+    u = c(m+2);
+end
+coff = c(1:m+1);
+err = u;

matlab数学建模算法/MATLAB语言常用算法程序集/第5章 函数逼近/multifit.m

@@ -1,3 +1,28 @@
-version https://git-lfs.github.com/spec/v1
-oid sha256:7c7114ce01ec338f77a0b7d1ee4a8f677ef30dc61ff39057ccf08d51f7f03f16
-size 472
+function A=multifit(X,Y,m)
+%A--�������϶���ʽ��ϵ��
+N=length(X);
+M=length(Y);
+if(N ~= M)
+    disp('���ݵ����겻ƥ�䣡');
+    return;
+end
+
+c(1:(2*m+1))=0;
+b(1:(m+1))=0;
+
+for j=1:(2*m+1)          %���c��b
+    for k=1:N
+        c(j)=c(j)+X(k)^(j-1);
+        if(j<(m+2))
+            b(j)=b(j)+Y(k)*X(k)^(j-1);
+        end
+    end
+end
+
+C(1,:)=c(1:(m+1));
+for s=2:(m+1)
+    C(s,:)=c(s:(m+s));
+end
+
+A=b'\C;                 %ֱ����ⷨ������ϵ��
+

matlab数学建模算法/MATLAB语言常用算法程序集/第6章 矩阵特征值计算/Chapoly.m

@@ -1,3 +1,9 @@
-version https://git-lfs.github.com/spec/v1
-oid sha256:f3b9e59fed41cd64c7a677b337855ce01ff77aaa42c36e2a02e3a35196fb381c
-size 142
+function l = Chapoly(A)
+syms t;
+
+N = size(A);
+n = N(1,1);
+
+y = det(A-t*eye(n,n));
+l = solve(y);
+l = vpa(l, 5);         %���ȡ��λ����

matlab数学建模算法/MATLAB语言常用算法程序集/第6章 矩阵特征值计算/dimethod.m

@@ -1,3 +1,31 @@
-version https://git-lfs.github.com/spec/v1
-oid sha256:c2949abcfb9abdf153c35963be343cfec45916ef00feb559ecda6b3c7dde2260
-size 574
+function [l,v]=dimethod(A,x0,u,eps)
+if nargin==3 
+    eps = 1.0e-6;
+end
+
+N = size(A);
+n = N(1,1);            %nΪA�Ľ�
+v = x0;              
+M = 5000;              %������������
+m = 0;      
+l = 0;
+for(k=1:M)
+    y = (A-u*eye(n,n))\v;
+    m = max(y);      %mΪ��ģ���ķ���
+    v = y/m;
+    
+    if(abs(m - l)<eps)
+        l = 1/m + u;       %�����辫�ȣ��˳�
+        return;
+    else
+        if(k==M)
+            disp('��������̫�࣬�����ٶ�̫����');
+            l = 1/m + u;
+        else
+            l = m;
+        end
+    end
+end
+
+
+        

matlab数学建模算法/MATLAB语言常用算法程序集/第6章 矩阵特征值计算/hessqrtz.m

@@ -1,3 +1,8 @@
-version https://git-lfs.github.com/spec/v1
-oid sha256:e9a856aec1d51df734e725aa046743834f1f8582574ef83b0e4991602fca5106
-size 109
+function l = hessqrtz(A,M)
+
+A = hess(A);
+for(i=1:M)
+    [q,r]=qr(A);
+    A = r*q;
+    l = diag(A);
+end

matlab数学建模算法/MATLAB语言常用算法程序集/第6章 矩阵特征值计算/ipmethod.m

@@ -1,3 +1,30 @@
-version https://git-lfs.github.com/spec/v1
-oid sha256:2e2ae443847f1f9f01bb493e9f2a88906a9f993e1390c9aba435a49466e5bda5
-size 519
+function [l,v]=ipmethod(A,x0,eps)
+if nargin==2 
+    eps = 1.0e-6;
+end
+
+v = x0;               
+M = 5000;              %������������
+m = 0; 
+l = 0;
+
+for(k=1:M)
+    y = A\v;
+    m = max(y);      %mΪ��ģ���ķ���
+    v = y/m;
+    
+    if(abs(m - l)<eps)
+        l = 1/m;   %�����辫�ȣ��˳���lΪ��ģ����С����ֵ
+        return;
+    else
+        if(k==M)
+            disp('��������̫�࣬�����ٶ�̫����');
+            l = 1/m;
+        else
+            l = m; 
+        end
+    end
+end
+
+
+        

matlab数学建模算法/MATLAB语言常用算法程序集/第6章 矩阵特征值计算/pmethod.m

@@ -1,3 +1,31 @@
-version https://git-lfs.github.com/spec/v1
-oid sha256:86cf22842625b709171f58eabd5d870a4368b48891a1c3517638ed4e148ba281
-size 583
+function [l,v,s]=pmethod(A,x0,eps)
+if nargin==2 
+    eps = 1.0e-6;
+end
+
+v = x0;               %v����������
+M = 5000;              %������������
+m = 0;      
+l = 0;
+for(k=1:M)
+    y = A*v;
+    m = max(y);      %mΪ��ģ���ķ���
+    v = y/m;
+    
+    if(abs(m - l)<eps)
+        l = m;       %�����辫�ȣ��˳���lΪ������ֵ
+        s = k;       %s��������
+        return;
+    else
+        if(k==M)
+            disp('��������̫�࣬�����ٶ�̫����');
+            l = m;
+            s = M;
+        else
+            l = m;
+        end
+    end
+end
+
+
+        

matlab数学建模算法/MATLAB语言常用算法程序集/第6章 矩阵特征值计算/qrtz.m

@@ -1,3 +1,7 @@
-version https://git-lfs.github.com/spec/v1
-oid sha256:85f80852da669ad4c0e1a730d8da269f92f78e8b9e020f85e1d432e71481ea23
-size 122
+function l = qrtz(A,M)
+
+for(i=1:M)                 %M��������
+    [q,r]=qr(A);
+    A = r*q;
+    l = diag(A);
+end

matlab数学建模算法/MATLAB语言常用算法程序集/第6章 矩阵特征值计算/rpmethod.m

@@ -1,3 +1,35 @@
-version https://git-lfs.github.com/spec/v1
-oid sha256:87b0078a02c315589a405329a0a430ea5881ce721f230afce4a3b95d6618f041
-size 612
+function [l,v,s]=rpmethod(A,x0,eps)
+if nargin==2 
+    eps = 1.0e-6;
+end
+
+v = x0;               %v����������
+M = 5000;              %������������
+m = 0; 
+l = 0;
+
+for(k=1:M)
+    y = A*v;
+    m = (y'*v)/(v'*v);      %m������
+    if(rank(m)>1)
+        m=(y*v')/(v*v');
+    end
+    v = y/m;
+    
+    if(abs(m - l)<eps)
+        l = m;   %�����辫�ȣ��˳���lΪ������ֵ
+        s = k;
+        return;
+    else
+        if(k==M)
+            disp('��������̫�࣬�����ٶ�̫����');
+            l = m;
+            s = M;
+        else
+            l = m; 
+        end
+    end
+end
+
+
+        

matlab数学建模算法/MATLAB语言常用算法程序集/第6章 矩阵特征值计算/rqrtz.m

@@ -1,3 +1,11 @@
-version https://git-lfs.github.com/spec/v1
-oid sha256:4481b517a7ffbe79743ece519100cbe1bcd8a580ba6ef0c0c1322469e48edf4f
-size 180
+function l = rqrtz(A,M)
+
+A = hess(A);
+for(i=1:M)
+    N = size(A);
+    n = N(1,1);
+    u = A(n,n);
+    [q,r]=qr(A-u*eye(n,n));
+    A = r*q+u*eye(n,n);
+    l = diag(A);
+end

matlab数学建模算法/MATLAB语言常用算法程序集/第6章 矩阵特征值计算/spmethod.m

@@ -1,3 +1,22 @@
-version https://git-lfs.github.com/spec/v1
-oid sha256:0a05c935c6d95c46f306353cb7c6b0f3925a2140c0dc4733d09a25fd6e27965a
-size 521
+function T=spmethod(A,eps)
+if nargin==1 
+    eps = 1.0e-6;
+end
+
+N = size(A);
+n = N(1,1);
+T = zeros(n,n);
+B = A;
+B1= B;
+
+for(i=1:n) 
+    s  = size(B);
+    r  = s(1,1);                             %rΪB�Ľ�
+    [T(i,i),u] = pmethod(B,ones(r,1),eps);   %���ݷ����������ֵ������������ 
+    u = u/u(1,1);                            %��������������һ��
+    B1 = B - u*B(1,:);                       
+    s1  = size(B1);
+    r1  = s(1,1);
+    B  = B1(2:r1,2:r1);                      %BΪ������ľ���
+end
+

matlab数学建模算法/MATLAB语言常用算法程序集/第7章 数值微分/CISimpson.m

@@ -1,3 +1,56 @@
-version https://git-lfs.github.com/spec/v1
-oid sha256:8f38c925fdab2fe75ace37a9ce069619cf6c197909500410a1e863148ea69766
-size 1388
+function df=CISimpson(func,x0,n,h)
+if nargin == 2                      %�����Dz������жϹ���
+    h = 0.1;
+    n = 5;
+else
+    if (nargin == 3 )
+        if (n<5)
+            disp('n������5!');
+            return;
+        else
+            h = 0.1;
+        end
+    else (nargin == 4 && h == 0.0)
+        disp('h����Ϊ0��');
+        return;
+    end
+end
+
+for(i=1:n)                        %���ѭ������ڵ�ĺ���ֵ
+     if (mod(n,2) == 0)
+        y(i)= subs(sym(func), findsym(sym(func)),x0+(i-n/2)*h);
+    else
+        y(i)= subs(sym(func), findsym(sym(func)),x0+(i-(n+1)/2)*h); 
+     end
+end
+
+f(1)=(y(3)-y(1))/(2*h);
+f(2)=(y(n)-y(n-2))/(2*h);           %������������΢�ַ������˵�ĵ���
+
+b(1:n-2,1) = zeros(n-2,1);
+b(1,1)=3*(y(3)-y(1))/h-f(1);
+b(n-2,1)=3*(y(n)-y(n-2))/h-f(2);   
+for(i=2:(n-3))
+    b(i,1) = 3*(y(i+2)-y(i))/h;
+end                                %��һ��������ɭ��ʽ���ұߵ�������
+
+for(i=1:n-2)
+    for(j=1:n-2)
+        if( (i == j+1) || (j == i+1))
+             A(i,j)= 1;
+        else if( i == j)
+             A(i,j) = 4;
+            end
+        end
+    end
+end                                %��һ����ϵ������  
+
+[Q,R]=qr(A);
+DF = R\(Q\b);                      %��QR�ֽⷨ���
+
+if( mod(n,2) == 0)
+    df = DF(n/2);
+else
+    df = DF((n+1)/2);             
+end                                %���������x0���ĵ���ֵ
+

matlab数学建模算法/MATLAB语言常用算法程序集/第7章 数值微分/DISimpson.m

@@ -1,3 +1,46 @@
-version https://git-lfs.github.com/spec/v1
-oid sha256:a90d3ef2f4ceae7871860f21cab63ea7d2c533b6a1ac10d66a0a22eea6f0ecf4
-size 716
+function df = DISimpson(X,Y,n,p)
+if n < 5
+    disp('n������5!');
+    return;
+end
+
+if p == 0
+    disp('p���ܵ���0!');
+    return;
+end
+
+h = X(2)-X(1);
+xx =linspace(X(1),X(n),h);
+if(xx ~= X)
+    disp('�ڵ�֮�䲻�ǵȾ�ģ�');
+    return;
+end
+
+f(1)=(Y(3)-Y(1))/(2*h);
+f(2)=(Y(n)-Y(n-2))/(2*h);
+b(1,1)=3*(Y(3)-Y(1))/h-f(1);
+b(n-2,1)=3*(Y(n)-Y(n-2))/h-f(2);
+for(i=2:n-3)
+    b(i,1) = 3*(Y(i+2)-Y(i))/h;
+end
+
+for(i=1:n-2)
+    for(j=1:n-2)
+        if( (i == j+1) || (j == i+1))
+             A(i,j) = 1;
+        else if( i == j)
+             A(i,j) = 4;
+            end
+        end
+    end
+end
+
+[Q,R]=qr(A);
+DF = R\(Q\b);
+
+if( p == 1)
+    df = f(1);
+else
+    df = DF(p-1);
+end
+

matlab数学建模算法/MATLAB语言常用算法程序集/第7章 数值微分/Diff2BSample.m

@@ -1,3 +1,33 @@
-version https://git-lfs.github.com/spec/v1
-oid sha256:46b8784a2f2d139a5e759303d354fe678d92e064a03f1554e73a79d81ee0d43e
-size 806
+function df0 = Diff2BSample(func,x0,n,h)
+format long;
+node_num = 2*n + 1;
+for i=1:node_num
+     y(i) = subs(sym(func), findsym(sym(func)), x0-n*h+i*h-h);
+end
+
+y_1 = (-3*y(1)+4*y(2)-y(3))/(2*h);
+y_N = (3*y(2*n+1)-4*y(2*n)+3*y(2*n-1))/(2*h);
+c = SubBSample(h,2*n,y,y_1,y_N);
+df0 = (y(n+1)-c(n+2))*6/h/h;
+format short;
+
+function c = SubBSample(h,n,y,y_1,y_N)
+f0 = 0.0;
+c = zeros(n+3,1);
+b = zeros(n+1,1);
+
+
+A = diag(4*ones(n+1,1));
+I = eye(n+1,n+1);
+AL = [I(2:n+1,:);zeros(1,n+1)];
+AU = [zeros(1,n+1);I(1:n,:)];
+A = A+AL+AU;                      %�γ�ϵ������
+for i=2:n
+    b(i,1) = 6*y(i);
+end
+b(1) = 6*y(1)+2*h*y_1;
+b(n+1) = 6*y(n+1)-2*h*y_N;
+d = followup(A,b);          %��׷�Ϸ����ϵ��
+c(2:n+2) = d;
+c(1) = c(2) - 2*h*y_1;      %c(-1)
+c(n+3) = c(3)+2*h*y_N;      %c(n+1)

matlab数学建模算法/MATLAB语言常用算法程序集/第7章 数值微分/DiffBSample.m

@@ -1,3 +1,33 @@
-version https://git-lfs.github.com/spec/v1
-oid sha256:242759d420d15a27098961b9a555a77420927080090c1c82e7e5b7d16142b1c6
-size 804
+function df0 = DiffBSample(func,x0,n,h) 
+format long;
+node_num = 2*n + 1;
+for i=1:node_num
+     y(i) = subs(sym(func), findsym(sym(func)), x0-n*h+i*h-h);
+end
+
+y_1 = (-3*y(1)+4*y(2)-y(3))/(2*h);
+y_N = (3*y(2*n+1)-4*y(2*n)+3*y(2*n-1))/(2*h);
+c = SubBSample(h,2*n,y,y_1,y_N);
+df0 = (c(n+3)-c(n+1))/2/h;
+format short;
+
+function c = SubBSample(h,n,y,y_1,y_N)
+f0 = 0.0;
+c = zeros(n+3,1);
+b = zeros(n+1,1);
+
+
+A = diag(4*ones(n+1,1));
+I = eye(n+1,n+1);
+AL = [I(2:n+1,:);zeros(1,n+1)];
+AU = [zeros(1,n+1);I(1:n,:)];
+A = A+AL+AU;                      %�γ�ϵ������
+for i=2:n
+    b(i,1) = 6*y(i);
+end
+b(1) = 6*y(1)+2*h*y_1;
+b(n+1) = 6*y(n+1)-2*h*y_N;
+d = followup(A,b);          %��׷�Ϸ����ϵ��
+c(2:n+2) = d;
+c(1) = c(2) - 2*h*y_1;      %c(-1)
+c(n+3) = c(3)+2*h*y_N;      %c(n+1)

matlab数学建模算法/MATLAB语言常用算法程序集/第7章 数值微分/FivePoint.m

@@ -1,3 +1,35 @@
-version https://git-lfs.github.com/spec/v1
-oid sha256:7f77700ba5398ad5df6165fe3925c69b484105b2e53d99f2123371bd9fcc8e0f
-size 1121
+function df=FivePoint(func,x0,type,h)
+if nargin == 3 
+    h = 0.1;
+else if (nargin == 4 && h == 0.0)
+        disp('h����Ϊ0��');
+        return;
+    end
+end
+
+y0 = subs(sym(func), findsym(sym(func)),x0);
+y1 = subs(sym(func), findsym(sym(func)),x0+h);
+y2 = subs(sym(func), findsym(sym(func)),x0+2*h);
+y3 = subs(sym(func), findsym(sym(func)),x0+3*h);
+y4 = subs(sym(func), findsym(sym(func)),x0+4*h);
+y_1 = subs(sym(func), findsym(sym(func)),x0-h);
+y_2 = subs(sym(func), findsym(sym(func)),x0-2*h);
+y_3 = subs(sym(func), findsym(sym(func)),x0-3*h);
+y_4 = subs(sym(func), findsym(sym(func)),x0-4*h);
+
+switch type
+    case 1,
+        df = (-25*y0+48*y1-36*y2+16*y3-3*y4)/(12*h);   %�õ�һ����ʽ����
+       
+    case 2,
+        df = (-3*y_1-10*y0+18*y1-6*y2+y3)/(12*h);     %�õڶ�����ʽ����
+        
+    case 3,
+        df = (y_2-8*y_1+8*y1-y2)/(12*h);               %�õ�������ʽ����
+         
+    case 4,
+        df = (3*y1+10*y0-18*y_1+6*y_2-y_3)/(12*h);    %�õ��ĸ���ʽ����
+             
+    case 5,
+        df = (25*y0-48*y_1+36*y_2-16*y_3+3*y_4)/(12*h);  %�õ������ʽ����
+end

matlab数学建模算法/MATLAB语言常用算法程序集/第7章 数值微分/FivePoint2.m

@@ -1,3 +1,30 @@
-version https://git-lfs.github.com/spec/v1
-oid sha256:e33ff90751958b45b7695dcff02a7076fda6d845d545d2853f1c03a50efe2645
-size 817
+function df= FivePoint2(func,x0,type,h)
+if nargin == 3 
+    h = 0.1;
+else if (nargin == 4 && h == 0.0)
+        disp('h����Ϊ0��');
+        return;
+    end
+end
+
+for i=1:9
+     y(i) = subs(sym(func), findsym(sym(func)), x0-4*h+i*h-h);
+end
+hd = 1/12/h/h;
+
+switch type
+    case 1,
+        df = (35*y(5)-104* y(6)+114* y(7)-56* y(8)+11* y(9))*hd;   %�õ�һ����ʽ����
+       
+    case 2,
+        df = (11*y(4)-20* y(5)+6* y(6)+4* y(7)- y(8))*hd;     %�õڶ�����ʽ����
+        
+    case 3,
+        df = (-y(3)+16* y(4)-30* y(5)+16* y(6)- y(7))*hd;       %�õ�������ʽ����
+         
+    case 4,
+        df = (-y(2)+4*y(3)-6*y(4)+20*y(5)+11*y(6))*hd;    %�õ��ĸ���ʽ����
+             
+    case 5,
+        df = (35*y(5)-104* y(4)+114* y(3)-56* y(2)+11* y(1))*hd;  %�õ������ʽ����
+end

matlab数学建模算法/MATLAB语言常用算法程序集/第7章 数值微分/FourPoint.m

@@ -1,3 +1,31 @@
-version https://git-lfs.github.com/spec/v1
-oid sha256:ba9cbd0bea91febf42fd22c59074aed24540b91741464145875a017def388d9e
-size 706
+function df= FourPoint(func,x0,type,h)
+%�����ĵ㷨����func��x0���Ķ��׵���
+%������: func
+%�󵼵�: x0
+%�ĵ㷨����ʽ�� type
+%���� ��h
+%����ֵ�� df
+if nargin == 3 
+    h = 0.1;
+else if (nargin == 4 && h == 0.0)
+        disp('h����Ϊ0��');
+        return;
+    end
+end
+
+for i=1:7
+     y(i) = subs(sym(func), findsym(sym(func)), x0-3*h+i*h-h);
+end
+hd = 1/6/h/h;
+
+switch type
+    case 1,
+        df = (12*y(4) - 30*y(5) + 24*y(6) - 6*y(7))*hd;   %�õ�һ����ʽ����
+       
+    case 2,
+        df = (6*y(3) - 12*y(4) + 6*y(5))*hd;     %�õڶ�����ʽ����
+        
+    case 3,
+        df = (12*y(4) - 30*y(3) + 24*y(2) - 6*y(1))*hd;               %�õ�������ʽ����
+         
+end

matlab数学建模算法/MATLAB语言常用算法程序集/第7章 数值微分/FourPoint2.m

@@ -1,3 +1,24 @@
-version https://git-lfs.github.com/spec/v1
-oid sha256:91b600f81184230e8ceb1339ff9d7b93664d6ad83b2aa630b89ab81283073c20
-size 587
+function df= FourPoint2(func,x0,type,h)
+if nargin == 3 
+    h = 0.1;
+else if (nargin == 4 && h == 0.0)
+        disp('h����Ϊ0��');
+        return;
+    end
+end
+
+for i=1:7
+     y(i) = subs(sym(func), findsym(sym(func)), x0-3*h+i*h-h);
+end
+hd = 1/6/h/h;
+
+switch type
+    case 1,
+        df = (12*y(4) - 30*y(5) + 24*y(6) - 6*y(7))*hd;   %�õ�һ����ʽ����׵���
+       
+    case 2,
+        df = (6*y(3) - 12*y(4) + 6*y(5))*hd;          %�õڶ�����ʽ����׵���
+        
+    case 3,
+        df = (12*y(4) - 30*y(3) + 24*y(2) - 6*y(1))*hd;   %�õ�������ʽ����׵���
+end

matlab数学建模算法/MATLAB语言常用算法程序集/第7章 数值微分/MidPoint.m

@@ -1,3 +1,12 @@
-version https://git-lfs.github.com/spec/v1
-oid sha256:22b8f25c015e441b4a28e55b0c909bd94e99036e7e99bfc59943e26f86df6b6f
-size 276
+function df=MidPoint(func,x0,h)
+if nargin == 2 
+    h = 0.1;
+else if (nargin == 3 && h == 0.0)
+        disp('h����Ϊ0��');
+        return;
+    end
+end
+
+y1 = subs(sym(func), findsym(sym(func)),x0+h);
+y2 = subs(sym(func), findsym(sym(func)),x0-h);
+df = (y1-y2)/(2*h);

matlab数学建模算法/MATLAB语言常用算法程序集/第7章 数值微分/Richason.m

@@ -1,3 +1,24 @@
-version https://git-lfs.github.com/spec/v1
-oid sha256:b68809b79cce5f26cd9462eb6dc26f23a41c34d23d368ec24738c787eedd1cd5
-size 556
+function df = Richason(func, x0, n, h)
+if nargin == 3 
+    h = 1;
+else if (nargin == 3 && h == 0.0)
+        disp('h����Ϊ0��');
+        return;
+    end
+end
+
+for(i=1:n)
+    y1 = subs(sym(func), findsym(sym(func)),x0+h/(2^i));
+    y2 = subs(sym(func), findsym(sym(func)),x0-h/(2^i));
+    G(i) = 2^(i-1)*(y1-y2)/h;            %��ý������ĵײ�ֵ
+end
+
+G1 = G;
+for(i=1:n-1)
+    for(j=(i+1):n)
+        G1(j)=(G(j)-(0.5)^(2*i)*G(j-1))/(1-(0.5)^(2*i)); %��ý�������ÿ��ֵ
+    end
+    G = G1;
+end
+    
+df = G(n);    %����ֵ��������õ���ֵ

matlab数学建模算法/MATLAB语言常用算法程序集/第7章 数值微分/SmartDF.m

@@ -1,3 +1,31 @@
-version https://git-lfs.github.com/spec/v1
-oid sha256:69daa40b171c8c958ecb846572d727f132871d9d2fa77907c72f301f2a31a264
-size 624
+function df0 = SmartDF(func,x0,eps)
+format long;
+if nargin == 2
+    eps = 1.0e-4;
+end
+
+df0_tmp = Inf;    
+n = 2;
+h = 0.1;
+con = 1;
+
+while con
+    node_num = 2*n + 1;
+    hd = 1/2/h;
+    x = (x0-n*h):h:(x0+n*h);
+    for i=1:node_num
+        y(i) = subs(sym(func), findsym(sym(func)), x(i));
+    end
+
+    y_1 = (-3*y(1)+4*y(2)-y(3))*hd;
+    y_N = (3*y(node_num)-4*y(node_num-1)+3*y(node_num-2))*hd;
+    c = SubBSample(h,2*n,y,y_1,y_N);
+    df0 = (c(n+2)-c(n))*hd;
+    if abs(df0 - df0_tmp) <= eps
+        con = 0;
+    else
+        df0_tmp = df0;
+        n = n+4;
+        h = h*0.75;
+    end
+end

matlab数学建模算法/MATLAB语言常用算法程序集/第7章 数值微分/ThreePoint.m

@@ -1,3 +1,27 @@
-version https://git-lfs.github.com/spec/v1
-oid sha256:08024609d9af64cc55fd04c4e68567f645b878a1b19132065aad09102c9da33d
-size 689
+function df=ThreePoint(func,x0,type,h)
+if nargin == 3 
+    h = 0.1;
+else if (nargin == 4 && h == 0.0)
+        disp('h����Ϊ0��');
+        return;
+    end
+end
+
+y0 = subs(sym(func), findsym(sym(func)),x0);  
+y1 = subs(sym(func), findsym(sym(func)),x0+h);
+y2 = subs(sym(func), findsym(sym(func)),x0+2*h);
+y_1 = subs(sym(func), findsym(sym(func)),x0-h);
+y_2 = subs(sym(func), findsym(sym(func)),x0-2*h);
+
+switch type
+    case 1,
+        df = (-3*y0+4*y1-y2)/(2*h);     %�õ�һ����ʽ����
+       
+    case 2,
+        df = (3*y0-4*y_1+y_2)/(2*h);   %�õڶ�����ʽ����
+      
+    case 3,
+        df = (y1-y_1)/(2*h);             %�õ�������ʽ����
+      
+end
+        

matlab数学建模算法/MATLAB语言常用算法程序集/第7章 数值微分/ThreePoint2.m

@@ -1,3 +1,25 @@
-version https://git-lfs.github.com/spec/v1
-oid sha256:93362e823211229c8114481d6131985303cb61a3c28340b556dce35af56c729c
-size 560
+function df= ThreePoint2(func,x0,type,h)
+if nargin == 3 
+    h = 0.1;
+else if (nargin == 4 && h == 0.0)
+        disp('h����Ϊ0��');
+        return;
+    end
+end
+
+for i=1:5
+     y(i) = subs(sym(func), findsym(sym(func)), x0-2*h+i*h-h);
+end
+hd = 1/h/h;
+
+switch type
+    case 1,
+        df = (y(3) - 2*y(4) + y(5))*hd;   %�õ�һ����ʽ����׵���
+       
+    case 2,
+        df = (y(2) - 2*y(3) + y(4))*hd;          %�õڶ�����ʽ����׵���
+        
+    case 3,
+        df = (y(1) - 2*y(2) + y(3))*hd;   %�õ�������ʽ����׵���
+         
+end

matlab数学建模算法/MATLAB语言常用算法程序集/第8章 数值积分/CombineTraprl.m

@@ -1,3 +1,30 @@
-version https://git-lfs.github.com/spec/v1
-oid sha256:cab5e6e104f2539c23633a161e416748762068b0e96b1b81b54d97ae75fa9dcb
-size 518
+function [I,step] = CombineTraprl(f,a,b,eps)
+%f    ��������
+%a,b  ����������
+%eps  ����
+%I    ���ֽ��
+%step ���ֵ���������
+if(nargin ==3)
+    eps=1.0e-4;
+end
+
+n=1;
+h=(b-a)/2;
+I1=0;
+I2=(subs(sym(f),findsym(sym(f)),a)+subs(sym(f),findsym(sym(f)),b))/h;
+while abs(I2-I1)>eps
+    n=n+1;  
+    h=(b-a)/n;
+    I1=I2;
+    I2=0;
+    for i=0:n-1
+        x=a+h*i;
+        x1=x+h;
+        I2=I2+(h/2)*(subs(sym(f),findsym(sym(f)),x)+subs(sym(f),findsym(sym(f)),x1));
+    end
+end
+
+I=I2;
+step=n;
+
+    

matlab数学建模算法/MATLAB语言常用算法程序集/第8章 数值积分/DDBuer.m

@@ -1,3 +1,30 @@
-version https://git-lfs.github.com/spec/v1
-oid sha256:b2bbb635a0f36f61afcf3740b6e12289fd76543a8a252854259ccddeb4c6e7b8
-size 673
+function [I,step] = DDBuer(f,a,b,eps)
+if(nargin==3)
+    eps=1.0e-4;
+end;
+n=1;
+h=b-a;
+I1=0;
+I2=(subs(sym(f),findsym(sym(f)),a)+subs(sym(f),findsym(sym(f)),b))/h/2;
+tol=1;
+while tol>eps
+    n=n+1;
+    h=h/4;
+    I1=I2;
+    I2=0;
+    for i=0:(4^(n-1)-1)
+        x=a+h*4*i;
+        x1=x+h;
+        x2=x1+h;
+        x3=x2+h;
+        x4=x3+h;
+        I2=I2+(2*h/45)*(7*subs(sym(f),findsym(sym(f)),x)+...
+            32*subs(sym(f),findsym(sym(f)),x1)+...
+            12*subs(sym(f),findsym(sym(f)),x2)+...
+            32*subs(sym(f),findsym(sym(f)),x3)+...
+            7*subs(sym(f),findsym(sym(f)),x4));
+    end
+    tol=abs(I2-I1);
+end
+I=I2;
+step=n;

matlab数学建模算法/MATLAB语言常用算法程序集/第8章 数值积分/DDSimpson.m

@@ -1,3 +1,27 @@
-version https://git-lfs.github.com/spec/v1
-oid sha256:f7e19d1dad409599a4a3dbca8a4211e17c316a2696c97d0f790baa6ac74f0e70
-size 537
+function [I,step] = DDSimpson(f,a,b,eps)
+if(nargin==3)
+    eps=1.0e-4;
+end;
+n=1;
+h=b-a;
+I1=0;
+I2=(subs(sym(f),findsym(sym(f)),a)+...
+    subs(sym(f),findsym(sym(f)),b))/h/2;
+tol=1;
+while tol>eps
+    n=n+1;
+    h=h/2;
+    I1=I2;
+    I2=0;
+    for i=0:(2^(n-1)-1)
+        x=a+h*2*i;
+        x1=x+h;
+        x2=x1+h;
+        I2=I2+(h/3)*(subs(sym(f),findsym(sym(f)),x)+...
+            4*subs(sym(f),findsym(sym(f)),x1)+...
+            subs(sym(f),findsym(sym(f)),x2));
+    end
+    tol=abs(I2-I1);
+end
+I=I2;
+step=n;

matlab数学建模算法/MATLAB语言常用算法程序集/第8章 数值积分/DDTraprl.m

@@ -1,3 +1,24 @@
-version https://git-lfs.github.com/spec/v1
-oid sha256:87c6dbceaa0dfeaeb56e3a924cd2936aaa90abcbb6807b0786937ef5987fd506
-size 497
+function [I,step] = DDTraprl(f,a,b,eps)
+if(nargin==3)
+    eps=1.0e-4;
+end;
+n=0;
+h=(b-a);
+I2=(subs(sym(f),findsym(sym(f)),a)+subs(sym(f),findsym(sym(f)),b))/h/2;
+tol=1;
+while tol>eps
+    n=n+1;
+    h=h/2;                  %������ηְ�
+    I1=I2;
+    I2=0;
+    for i=0:(2^n-1)
+        x=a+h*i;
+        x1=x+h;
+        I2=I2+(h/2)*(subs(sym(f),findsym(sym(f)),x)+...
+            subs(sym(f),findsym(sym(f)),x1));        %���ι�ʽ
+    end
+    tol=abs(I2-I1);
+end
+
+I=I2;
+step=n;

matlab数学建模算法/MATLAB语言常用算法程序集/第8章 数值积分/DblSimpson.m

@@ -1,3 +1,37 @@
-version https://git-lfs.github.com/spec/v1
-oid sha256:2c4f093879a0c64ff489c3a7ec36a74db4822627b42a9c027a88cc69bc173d1e
-size 1483
+function q=DblSimpson(f,a,A,b,B,m,n)
+if(m==1 && n==1)           %����ɭ��ʽ
+    q=((B-b)*(A-a)/9)*(subs(sym(f),findsym(sym(f)),{a,b})+...
+        subs(sym(f),findsym(sym(f)),{a,B})+...
+        subs(sym(f),findsym(sym(f)),{A,b})+...
+        subs(sym(f),findsym(sym(f)),{A,B})+...
+        4*subs(sym(f),findsym(sym(f)),{(A-a)/2,b})+...
+        4*subs(sym(f),findsym(sym(f)),{(A-a)/2,B})+...
+        4*subs(sym(f),findsym(sym(f)),{a,(B-b)/2})+...
+        4*subs(sym(f),findsym(sym(f)),{A,(B-b)/2})+...
+        16*subs(sym(f),findsym(sym(f)),{(A-a)/2,(B-b)/2}));
+    
+else                       %��������ɭ��ʽ
+    q=0;
+    for i=0:n-1
+        for j=0:m-1
+            x=a+2*i*(A-a)/2/n;
+            y=b+2*j*(B-b)/2/m;            
+            x1=a+(2*i+1)*(A-a)/2/n;
+            y1=b+(2*j+1)*(B-b)/2/m;
+            x2=a+2*(i+1)*(A-a)/2/n;
+            y2=b+2*(j+1)*(B-b)/2/m;
+            
+            q=q+subs(sym(f),findsym(sym(f)),{x,y})+...
+                subs(sym(f),findsym(sym(f)),{x,y2})+...
+                subs(sym(f),findsym(sym(f)),{x2,y})+...
+                subs(sym(f),findsym(sym(f)),{x2,y2})+...
+                4*subs(sym(f),findsym(sym(f)),{x,y1})+...
+                4*subs(sym(f),findsym(sym(f)),{x2,y1})+...
+                4*subs(sym(f),findsym(sym(f)),{x1,y})+...
+                4*subs(sym(f),findsym(sym(f)),{x1,y2})+...
+                16*subs(sym(f),findsym(sym(f)),{x1,y1});
+        end
+   end
+end
+
+q=((B-b)*(A-a)/36/m/n)*q;

matlab数学建模算法/MATLAB语言常用算法程序集/第8章 数值积分/DblTraprl.m

@@ -1,3 +1,31 @@
-version https://git-lfs.github.com/spec/v1
-oid sha256:db9423d111cbcc8ee3d627881b8c5b93cd6a98238834ab5ad10c46ed25cb8540
-size 733
+function q=DblTraprl(f,a,A,b,B,m,n)
+if(m==1 && n==1)           %���ι�ʽ
+    q=((B-b)*(A-a)/4)*(subs(sym(f),findsym(sym(f)),{a,b})+...
+        subs(sym(f),findsym(sym(f)),{a,B})+...
+        subs(sym(f),findsym(sym(f)),{A,b})+...
+        subs(sym(f),findsym(sym(f)),{A,B}));
+    
+else                       %�������ι�ʽ
+    C=4*ones(n+1,m+1);
+    C(1,:)=2;
+    C(:,1)=2;
+    C(n+1,:)=2;
+    C(:,m+1)=2;
+    C(1,1)=1;
+    C(1,m+1)=1;
+    C(n+1,1)=1;
+    C(n+1,m+1)=1;           %C����
+end
+
+F=zeros(n+1,m+1);
+q=0;
+for i=0:n
+   for j=0:m
+       x=a+i*(A-a)/n;
+       y=b+j*(B-b)/m;
+       F(i+1,j+1)=subs(sym(f),findsym(sym(f)),{x,y});
+       q=q+F(i+1,j+1)*C(i+1,j+1);
+   end
+end
+
+q=((B-b)*(A-a)/4/m/n)*q;

matlab数学建模算法/MATLAB语言常用算法程序集/第8章 数值积分/IntDBGauss.m

@@ -1,3 +1,23 @@
-version https://git-lfs.github.com/spec/v1
-oid sha256:2329c20c12dba2a33311abc291afdad4224fbb5ddc3d6959506c83178e98deb8
-size 797
+function q = IntDBGauss(func,a,b,c,d,m,n)
+format long;
+ta = (b-a)/2;
+tb = (a+b)/2;
+tc = (d-c)/2;
+td = (c+d)/2;
+f = zeros(n,m);
+node_x = [0 0 0 0 0;-0.5773503  0.5773503 0 0 0;-0.7745967  0  0.7745967  0 0;
+         -0.8611363  -0.3398810  0.3398810  0.8611363 0;
+         -0.9061793  -0.5384693  0  0.5384693  0.9061793];   %��˹���ֵ��������
+node_A = [2 0 0 0 0;1  1 0 0 0;0.5555556  0.8888889  0.5555556   0 0;
+         0.3478548  0.6521453   0.6521453  0.3478548  0;
+         0.2369269  0.4786287  0.5688889  0.4786287  0.2369269];
+            %��˹����ϵ������
+for i=1:m
+   for j=1:n
+       f(j,i) = subs(sym(func),findsym(sym(func)),[ta*node_x(m,i)+tb tc*node_x(n,i)+td]);
+   end
+end
+Am = transpose(node_A(m,1:m));
+An = node_A(n,1:n);
+q =ta*tc* An*f*Am;
+format short;

matlab数学建模算法/MATLAB语言常用算法程序集/第8章 数值积分/IntGauss.m

@@ -1,3 +1,41 @@
-version https://git-lfs.github.com/spec/v1
-oid sha256:0f8d62b90e3601b672fa2924d19beb8254bf18a6a43321ca38e6dccb7f542860
-size 1386
+function I = IntGauss(f,a,b,n,AK,XK)
+if(n<5 && nargin == 4)
+    AK = 0;
+    XK = 0;
+else
+    XK1=((b-a)/2)*XK+((a+b)/2);
+    I=((b-a)/2)*sum(AK.*subs(sym(f),findsym(f),XK1));
+end
+
+ta = (b-a)/2;
+tb = (a+b)/2;
+switch n
+    case 0,
+        I=2*ta*subs(sym(f),findsym(sym(f)),tb);
+        
+    case 1,
+        I=ta*(subs(sym(f),findsym(sym(f)),ta*0.5773503+tb)+...
+            subs(sym(f),findsym(sym(f)),-ta*0.5773503+tb));
+        
+    case 2,
+        I=ta*(0.55555556*subs(sym(f),findsym(sym(f)),ta*0.7745967+tb)+...
+            0.55555556*subs(sym(f),findsym(sym(f)),-ta*0.7745967+tb)+...
+            0.88888889*subs(sym(f),findsym(sym(f)),tb));
+           
+    case 3,
+        I=ta*(0.3478548*subs(sym(f),findsym(sym(f)),ta*0.8611363+tb)+...
+            0.3478548*subs(sym(f),findsym(sym(f)),-ta*0.8611363+tb)+...
+            0.6521452*subs(sym(f),findsym(sym(f)),ta*0.3398810+tb)...
+            +0.6521452*subs(sym(f),findsym(sym(f)),-ta*0.3398810+tb));
+  
+        
+    case 4,
+        I=ta*(0.2369269*subs(sym(f),findsym(sym(f)),ta*0.9061793+tb)+...
+            0.2369269*subs(sym(f),findsym(sym(f)),-ta*0.9061793+tb)+...
+            0.4786287*subs(sym(f),findsym(sym(f)),ta*0.5384693+tb)...
+            +0.4786287*subs(sym(f),findsym(sym(f)),-ta*0.5384693+tb)+...
+            0.5688889*subs(sym(f),findsym(sym(f)),tb));
+end
+        
+
+        

matlab数学建模算法/MATLAB语言常用算法程序集/第8章 数值积分/IntGaussHermite.m

@@ -1,3 +1,31 @@
-version https://git-lfs.github.com/spec/v1
-oid sha256:d54acb989c2d14ee0e014b08c55f2a1f823255e7e46d3e7fd8a4a31e1aaf654c
-size 1079
+function I = IntGaussHermite(f,n,AK,XK)
+if(n<6 && nargin == 2)
+    AK = 0;
+    XK = 0;
+else
+    I=sum(AK.*subs(sym(f),findsym(sym(f)),XK));
+end
+
+switch n
+    case 2,
+        I=0.886227*(subs(sym(f),findsym(sym(f)),-0.707107)+...
+            subs(sym(f),findsym(sym(f)),0.707107));
+        
+    case 3,
+        I=1.181636*subs(sym(f),findsym(sym(f)),0)+...
+            0.295409*(subs(sym(f),findsym(sym(f)),1.224745)+...
+            subs(sym(f),findsym(sym(f)),-1.224745));
+        
+    case 4,
+        I=0.544444*(subs(sym(f),findsym(sym(f)),0.524648)+...
+            subs(sym(f),findsym(sym(f)),-0.524648))+...
+            0.100000*(subs(sym(f),findsym(sym(f)),1.650680)+...
+            subs(sym(f),findsym(sym(f)),-1.650680));
+           
+    case 5,
+        I=0.945309*subs(sym(f),findsym(sym(f)),0)+...
+            0.393619*(subs(sym(f),findsym(sym(f)),0.958572)+...
+            subs(sym(f),findsym(sym(f)),-0.958572))+...
+            0.199532*(subs(sym(f),findsym(sym(f)),2.020183)+...
+            subs(sym(f),findsym(sym(f)),-2.020183));  
+end

matlab数学建模算法/MATLAB语言常用算法程序集/第8章 数值积分/IntGaussLada.m

@@ -1,3 +1,35 @@
-version https://git-lfs.github.com/spec/v1
-oid sha256:61332ada613e1c995585aa048e7c0f8eb4a59cbe3ea129d3ec57238a3297aef9
-size 1338
+function I = IntGaussLada(f,a,b,n,AK,XK)
+if(n<6 && nargin == 4)
+    AK = 0;
+    XK = 0;
+else
+    XK1=((b-a)/2)*XK+((a+b)/2);
+    I=((b-a)/2)*((2/n/n)*subs(sym(f),findsym(sym(f)),a)+...
+    sum(AK.*subs(sym(f),findsym(sym(f)),XK1)));
+end
+
+ta = (b-a)/2;
+tb = (a+b)/2;
+switch n         
+    case 2,
+        I=ta*0.5*subs(sym(f),findsym(sym(f)),ta*(-1)+tb)+...
+            1.5*ta*subs(sym(f),findsym(sym(f)),ta*(1/3)+tb);
+        
+    case 3,
+        I=ta*((2/9)*subs(sym(f),findsym(sym(f)),ta*(-1)+tb)+...
+            0.752806*subs(sym(f),findsym(sym(f)),ta*(-0.289898)+tb)+...
+            1.024972*subs(sym(f),findsym(sym(f)),ta*0.689898+tb));
+        
+    case 4,
+        I=ta*(0.125*subs(sym(f),findsym(sym(f)),ta*(-1)+tb)+...
+            0.657689*subs(sym(f),findsym(sym(f)),-ta*0.575319+tb)+...
+            0.776387*subs(sym(f),findsym(sym(f)),ta*0.181066+tb)+...
+            0.440925*subs(sym(f),findsym(sym(f)),ta*0.822824+tb));
+           
+    case 5,
+        I=ta*(0.08*subs(sym(f),findsym(sym(f)),ta*(-1)+tb)+...
+            0.446207*subs(sym(f),findsym(sym(f)),-ta*0.720480+tb)+...
+            0.623653*subs(sym(f),findsym(sym(f)),-ta*0.167181+tb)+...
+            0.562712*subs(sym(f),findsym(sym(f)),ta*0.446314+tb)+...
+            0.287427*subs(sym(f),findsym(sym(f)),ta*0.885792+tb));     
+end

matlab数学建模算法/MATLAB语言常用算法程序集/第8章 数值积分/IntGaussLager.m

@@ -1,3 +1,31 @@
-version https://git-lfs.github.com/spec/v1
-oid sha256:0e2ffc28cb4e47e6a14e04525ab33bf2e21b3f69bb49fe013263dc7fc86c47e2
-size 1141
+function I = IntGaussLager(f,n,AK,XK)
+if(n<6 && nargin == 2)
+    AK = 0;
+    XK = 0;
+else
+    I=sum(AK.*subs(sym(f),findsym(sym(f)),XK));
+end
+
+switch n
+    case 2,
+        I=0.853553*subs(sym(f),findsym(sym(f)),-0.585786)+...
+            0.146447*subs(sym(f),findsym(sym(f)),3.414214);
+        
+    case 3,
+        I=0.711093*subs(sym(f),findsym(sym(f)),0.415575)+...
+            0.278518*subs(sym(f),findsym(sym(f)),2.294280)+...
+            0.0103893*subs(sym(f),findsym(sym(f)),6.289945);
+        
+    case 4,
+        I=0.603154*subs(sym(f),findsym(sym(f)),0.322548)+...
+            0.357419*subs(sym(f),findsym(sym(f)),1.745761)+...
+            0.0388879*subs(sym(f),findsym(sym(f)),4.536620)+...
+            0.000539295*subs(sym(f),findsym(sym(f)),9.395071);
+           
+    case 5,
+        I=0.521756*subs(sym(f),findsym(sym(f)),0.263560)+...
+            0.398667*subs(sym(f),findsym(sym(f)),1.413403)+...
+            0.0759424*subs(sym(f),findsym(sym(f)),3.596426)+...
+            0.00361176*subs(sym(f),findsym(sym(f)),7.085810)+...
+            0.0000233700*subs(sym(f),findsym(sym(f)),12.640801);  
+end

matlab数学建模算法/MATLAB语言常用算法程序集/第8章 数值积分/IntGaussLobato.m

@@ -1,3 +1,38 @@
-version https://git-lfs.github.com/spec/v1
-oid sha256:123c955d0949a96767b7960a7d0fc728412c886cc011eefd643425e912b50309
-size 1483
+function I = IntGaussLobato(f,a,b,n,AK,XK)
+if(n<7 && nargin == 4)
+    AK = 0;
+    XK = 0;
+else      
+    XK1=((b-a)/2)*XK+((a+b)/2);
+    I=((b-a)/2)*((2/n/(n-1))*(subs(sym(f),findsym(sym(f)),a)+...
+        subs(sym(f),findsym(sym(f)),b))+sum(AK.*subs(sym(f),findsym(sym(f)),XK1)));
+end
+
+ta = (b-a)/2;
+tb = (a+b)/2;
+switch n
+    case 3,
+        I=ta*((1/3)*(subs(sym(f),findsym(sym(f)),a)+...
+        subs(sym(f),findsym(sym(f)),b))+1.333333*subs(sym(f),findsym(sym(f)),tb));
+        
+    case 4,
+        I=ta*((1/6)*(subs(sym(f),findsym(sym(f)),a)+...
+            subs(sym(f),findsym(sym(f)),b))+0.833333*...
+            (subs(sym(f),findsym(sym(f)),ta*0.447214+tb)+...
+            subs(sym(f),findsym(sym(f)),-ta*0.447214+tb)));
+        
+    case 5,
+         I=ta*((1/10)*(subs(sym(f),findsym(sym(f)),a)+...
+             subs(sym(f),findsym(sym(f)),b))+0.544444*...
+            (subs(sym(f),findsym(sym(f)),ta*0.654654+tb)+...
+            subs(sym(f),findsym(sym(f)),-ta*0.654654+tb))+...
+            0.711111*subs(sym(f),findsym(sym(f)),tb));
+           
+    case 6,
+         I=ta*((1/15)*(subs(sym(f),findsym(sym(f)),a)+...
+             subs(sym(f),findsym(sym(f)),b))+0.554858*...
+            (subs(sym(f),findsym(sym(f)),ta*0.285232+tb)+...
+            subs(sym(f),findsym(sym(f)),-ta*0.285232+tb))+...
+            0.378475*(subs(sym(f),findsym(sym(f)),ta*0.765055+tb)+...
+            subs(sym(f),findsym(sym(f)),-ta*0.765055+tb)));     
+end

matlab数学建模算法/MATLAB语言常用算法程序集/第8章 数值积分/IntPWC.m

@@ -1,3 +1,22 @@
-version https://git-lfs.github.com/spec/v1
-oid sha256:a2faa03632a4b6f259422b1f061f055d1289e1c3c5e9ba6344deb5417bbcd623
-size 680
+function q = IntPWC(X,Y,n)
+format long;
+h = zeros(n-1,1);
+lamda = zeros(n,1);
+L = zeros(n-2,1);
+R = zeros(n-2,1);
+Dlta = zeros(n-2,1);
+h(1) = X(2)-X(1);
+for j=1:n-2          %����ÿ��������Ļ��ֲ���
+    h(j+1) = X(j+2)-X(j+1);
+    lamda(j) = h(j)/h(j+1);
+    Dlta(j) = h(j+1)/h(j);
+    L(j) = (Dlta(j)*Dlta(j))*Y(j)/(1+Dlta(j))-Dlta(j)*Y(j+1)+...
+           +Dlta(j)*Y(j+2)/(1+Dlta(j));
+    R(j) = (lamda(j)*lamda(j))*Y(j+2)/(1+lamda(j))-lamda(j)*Y(j+1)+...
+           +lamda(j)*Y(j)/(1+lamda(j));
+end
+q = h(1)*(3*Y(1)+3*Y(2)-R(1))/6+h(n-1)*(3*Y(n-1)+3*Y(n)-L(n-2))/6;
+for k=2:n-2
+    q = q + h(k)*(3*Y(k)+3*Y(k+1)-0.5*R(k)-0.5*L(k-1))/6;
+end
+format short;

matlab数学建模算法/MATLAB语言常用算法程序集/第8章 数值积分/IntQBXF1.m

@@ -1,3 +1,12 @@
-version https://git-lfs.github.com/spec/v1
-oid sha256:546ecc80282dd1ae498c8f0c7585d7fdcc2c185f2bf5b5fcb4839c3fb6823245
-size 253
+function q = IntQBXF1(func,n)
+format long;
+pi = 3.1415926535;
+q = 0;
+A = zeros(n,1);
+x = zeros(n,1);
+for i=1:n
+    A(i) = pi/n;
+    x(i) = cos(pi*(2*i-1)/2/n);
+    y(i) = subs(sym(func), findsym(sym(func)), x(i));
+    q = q + A(i)*y(i);
+end