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2,100 | Some basic information on information-based complexity theory | math.NA | Numerical analysts might be expected to pay close attention to a branch of
complexity theory called information-based complexity theory (IBCT), which
produces an abundance of impressive results about the quest for approximate
solutions to mathematical problems. Why then do most numerical analysts turn a
cold shoulder t... | math |
2,101 | Perspectives on information-based complexity | math.NA | The authors discuss information-based complexity theory, which is a model of
finite-precision computations with real numbers, and its applications to
numerical analysis. | math |
2,102 | Mathematical pressure volume models of the cerebrospinal fluid | math.NA | Numerous mathematical models have emerged in the medical literature over the
past two decades attempting to characterize the pressure and volume dynamics
the central nervous system compartment. These models have been used to study he
behavior of this compartment under such pathological clinical conditions s
hydrocephal... | math |
2,103 | Good rotations | math.NA | Numerical integrations in celestial mechanics often involve the repeated
computation of a rotation with a constant angle. A direct evaluation of these
rotations yields a linear drift of the distance to the origin. This is due to
roundoff in the representation of the sine s and cosine c of the angle theta.
In a computer... | math |
2,104 | Numerical Analysis of Two-Phase Flow in Gas-Dynamic Filter | math.NA | This paper presents numerical and analytical investigation of gas flow in
gas-dynamic filter - a device for cleaning gas from solid particles with
counter flow of large water particles in order to prevent their release to the
atmosphere.
Ideal and viscous gas flows are considered. It is assumed, that gas flow is
stat... | math |
2,105 | Approximate Models of Dynamic Thermoviscoelasticity Describing Shape-Memory-Alloy Phase Transitions | math.NA | We consider problems of dynamic viscoelasticity taking into account the
coupling of elastic and thermal fields. Efficient approximate models are
developed and computational results on thermomechanical behaviour of
shape-memory-alloy structures are presented. | math |
2,106 | Numerical Calculations Using Maple: Why & How? | math.NA | The possibility of interaction between Maple and numeric compiled languages
in performing extensive numeric calculations is exemplified by the Ndynamics
package, a tool for studying the (chaotic) behavior of dynamical systems.
Programming hints concerning the construction of Ndynamics are presented. The
system command,... | math |
2,107 | A multi-level algorithm for the solution of moment problems | math.NA | We study numerical methods for the solution of general linear moment
problems, where the solution belongs to a family of nested subspaces of a
Hilbert space. Multi-level algorithms, based on the conjugate gradient method
and the Landweber--Richardson method are proposed that determine the "optimal"
reconstruction level... | math |
2,108 | Rates of convergence for the approximation of dual shift-invariant systems in $l_2(Z)$ | math.NA | A shift-invariant system is a collection of functions $\{g_{m,n}\}$ of the
form $g_{m,n}(k) = g_m(k-an)$. Such systems play an important role in
time-frequency analysis and digital signal processing. A principal problem is
to find a dual system $\gamma_{m,n}(k) = \gamma_m(k-an)$ such that each
function $f$ can be writt... | math |
2,109 | A Levinson-Galerkin algorithm for regularized trigonometric approximation | math.NA | Trigonometric polynomials are widely used for the approximation of a smooth
function $f$ from a set of nonuniformly spaced samples
$\{f(x_j)\}_{j=0}^{N-1}$. If the samples are perturbed by noise, controlling
the smoothness of the trigonometric approximation becomes an essential issue to
avoid overfitting and underfitti... | math |
2,110 | On the fourth-order accurate compact ADI scheme for solving the unsteady Nonlinear Coupled Burgers' Equations | math.NA | The two-dimensional unsteady coupled Burgers' equations with moderate to
severe gradients, are solved numerically using higher-order accurate finite
difference schemes; namely the fourth-order accurate compact ADI scheme, and
the fourth-order accurate Du Fort Frankel scheme. The question of numerical
stability and conv... | math |
2,111 | Stochastic trace formulas | math.NA | The spectrum of the evolution Operator associated with a nonlinear stochastic
flow with additive noise is evaluated by diagonalization in a polynomial basis.
The method works for arbitrary noise strength. In the weak noise limit we
formulate a new perturbative expansion for the spectrum of the stochastic
evolution Oper... | math |
2,112 | Methods for the approximation of the matrix exponential in a Lie-algebraic setting | math.NA | Discretization methods for ordinary differential equations based on the use
of matrix exponentials have been known for decades. This set of ideas has come
off age and acquired greater urgency recently, within the context of geometric
integration and discretization methods on manifolds based on the use of
Lie-group acti... | math |
2,113 | Condition number bounds for problems with integer coefficients | math.NA | An apriori bound for the condition number associated to each of the following
problems is given: general linear equation solving, minimum squares,
non-symmetric eigenvalue problems, solving univariate polynomials, solving
systems of multivariate polynomials. It is assumed that the input has integer
coefficients and is ... | math |
2,114 | Lower bounds for some decision problems over C | math.NA | Lower bounds for some explicit decision problems over the complex numbers are
given. | math |
2,115 | Ultimate Polynomial Time | math.NA | The class $\mathcal{UP}$ of `ultimate polynomial time' problems over $\mathbb
C$ is introduced; it contains the class $\mathcal P$ of polynomial time
problems over $\mathbb C$.
The $\tau$-Conjecture for polynomials implies that $\mathcal{UP}$ does not
contain the class of non-deterministic polynomial time problems de... | math |
2,116 | A novel methodology of weighted residual for nonlinear computations | math.NA | One of strengths in the finite element (FE) and Galerkin methods is their
capability to apply weak formulations via integration by parts, which leads to
elements matching at lower degree of continuity and relaxes requirements of
choosing basis functions. However, when applied to nonlinear problems, the
methods of this ... | math |
2,117 | An efficient step size selection for ODE codes | math.NA | We give an algorithm for efficient step size control in numerical integration
of non-stiff initial value problems, based on a formula tailormade to methods
where the numerical solution is compared with a solution of lower order. | math |
2,118 | Generalized linearization of nonlinear algebraic equations: an innovative approach | math.NA | Based on the matrix expression of general nonlinear numerical analogues
presented by the present author, this paper proposes a novel philosophy of
nonlinear computation and analysis. The nonlinear problems are considered an
ill-posed linear system. In this way, all nonlinear algebraic terms are instead
expressed as Lin... | math |
2,119 | Reliable operations on oscillatory functions | math.NA | Approximate $p$-point Leibniz derivation formulas as well as interpolatory
Simpson quadrature sums adapted to oscillatory functions are discussed. Both
theoretical considerations and numerical evidence concerning the dependence of
the discretization errors on the frequency parameter of the oscillatory
functions show th... | math |
2,120 | Relationship formula between nonlinear polynomial equations and the corresponding Jacobian matrix | math.NA | This paper provides a general proof of a relationship theorem between
nonlinear analogue polynomial equations and the corresponding Jacobian matrix,
presented recently by the present author. This theorem is also verified
generally effective for all nonlinear polynomial algebraic system of equations.
As two particular a... | math |
2,121 | Pseudo-Newton method for nonlinear equations | math.NA | In order to avoid the evaluation of the Jacobian matrix and its inverse, the
present author recently introduced the pseudo-Jacobian matrix with a general
applicability of any nonlinear systems of equations. By using this concept,
this paper proposes the pseudo-Newton method | math |
2,122 | Implicit Integration of the Time-Dependent Ginzburg-Landau Equations of Superconductivity | math.NA | This article is concerned with the integration of the time-dependent
Ginzburg-Landau (TDGL) equations of superconductivity. Four algorithms, ranging
from fully explicit to fully implicit, are presented and evaluated for
stability, accuracy, and compute time. The benchmark problem for the evaluation
is the equilibration... | math |
2,123 | Antisymmetry, pseudospectral methods, and conservative PDEs | math.NA | `Dual composition', a new method of constructing energy-preserving
discretizations of conservative PDEs, is introduced. It extends the
summation-by-parts approach to arbitrary differential operators and conserved
quantities. Links to pseudospectral, Galerkin, antialiasing, and Hamiltonian
methods are discussed. | math |
2,124 | A modified BFGS quasi-Newton iterative formula | math.NA | The quasi-Newton equation is the very basis of a variety of the quasi-Newton
methods. By using a relationship formula between nonlinear polynomial equations
and the corresponding Jacobian matrix. presented recently by the present
author, we established an exact alternative of the approximate quasi-Newton
equation and c... | math |
2,125 | A new definition of nonlinear statistics mean and variance | math.NA | This note presents a new definition of nonlinear statistics mean and variance
to simplify the nonlinear statistics computations. These concepts aim to
provide a theoretical explanation of a novel nonlinear weighted residual
methodology presented recently by the present author. | math |
2,126 | Fast and accurate multigrid solution of Poissons equation using diagonally oriented grids | math.NA | We solve Poisson's equation using new multigrid algorithms that converge
rapidly. The novel feature of the 2D and 3D algorithms are the use of extra
diagonal grids in the multigrid hierarchy for a much richer and effective
communication between the levels of the multigrid. Numerical experiments
solving Poisson's equati... | math |
2,127 | On the Geometry of Graeffe Iteration | math.NA | A new version of the Graeffe algorithm for finding all the roots of
univariate complex polynomials is proposed. It is obtained from the classical
algorithm by a process analogous to renormalization of dynamical systems. This
iteration is called Renormalized Graeffe Iteration.
It is globally convergent, with probabili... | math |
2,128 | Tangent Graeffe Iteration | math.NA | Graeffe iteration was the choice algorithm for solving univariate polynomials
in the XIX-th and early XX-th century. In this paper, a new variation of
Graeffe iteration is given, suitable to IEEE floating-point arithmetics of
modern digital computers. We prove that under a certain generic assumption the
proposed algori... | math |
2,129 | High Accuracy Method for Integral Equations with Discontinuous Kernels | math.NA | A new highly accurate numerical approximation scheme based on a Gauss type
Clenshaw-Curtis Quadrature for Fredholm integral equations of the second kind,
whose kernel is either discontinuous or not smooth along the main diagonal, is
presented. This scheme is of spectral accuracy when the kernel is infinitely
differenti... | math |
2,130 | Prediction of large-scale dynamics using unresolved computations | math.NA | We present a theoretical framework and numerical methods for predicting the
large-scale properties of solutions of partial differential equations that are
too complex to be properly resolved. We assume that prior statistical
information about the distribution of the solutions is available, as is often
the case in pract... | math |
2,131 | The influence of the flow of the reacting gas on the conditions for a Thermal Explosion | math.NA | The classical problem of thermal explosion is modified so that the chemically
active gas is not at rest but is flowing in a long cylindrical pipe. Up to a
certain section the heat-conducting walls of the pipe are held at low
temperature so that the reaction rate is small and there is no heat release; at
that section th... | math |
2,132 | The Kolmogorov-Obukhov Exponent in the Inertial Range of Turbulence: A Reexamination of Experimental Data | math.NA | In recent papers Benzi et al. presented experimental data and an analysis to
the effect that the well-known "2/3" Kolmogorov-Obukhov exponent in the
inertial range of local structure in turbulence should be corrected by a small
but definitely non-zero amount. We reexamine the very same data and show that
this conclusio... | math |
2,133 | A numerical scheme for impact problems | math.NA | We consider a mechanical system with impact and n degrees of freedom, written
in generalized coordinates. The system is not necessarily Lagrangian. The
representative point of the system must remain inside a set of constraints K;
the boundary of K is three times differentiable.
At impact, the tangential component of ... | math |
2,134 | Optimal prediction and the Klein-Gordon equation | math.NA | The method of optimal prediction is applied to calculate the future means of
solutions to the Klein-Gordon equation. It is shown that in an appropriate
probability space, the difference between the average of all solutions that
satisfy certain constraints at time t=0, and the average computed by an
approximate method, ... | math |
2,135 | Compact Central WENO Schemes for Multidimensional Conservation Laws | math.NA | We present a new third-order central scheme for approximating solutions of
systems of conservation laws in one and two space dimensions. In the spirit of
Godunov-type schemes,our method is based on reconstructing a
piecewise-polynomial interpolant from cell-averages which is then advanced
exactly in time. In the recons... | math |
2,136 | Optimal Prediction for Hamiltonian partial differential equations | math.NA | Optimal prediction methods compensate for a lack of resolution in the
numerical solution of time-dependent differential equations through the use of
prior statistical information. We present a new derivation of the basic
methodology, show that field-theoretical perturbation theory provides a useful
device for dealing w... | math |
2,137 | Mathematical Modeling of Boson-Fermion Stars in the Generalized Scalar-Tensor Theories of Gravity | math.NA | A model of static boson-fermion star with spherical symmetry based on the
scalar-tensor theory of gravity with massive dilaton field is investigated
numerically.
Since the radius of star is \textit{a priori} an unknown quantity, the
corresponding boundary value problem (BVP) is treated as a nonlinear spectral
problem... | math |
2,138 | Numerical Investigation of a Dipole Type Solution for Unsteady Groundwater Flow with Capillary Retention and Forced Drainage | math.NA | A model of unsteady filtration (seepage) in a porous medium with capillary
retention is considered. It leads to a free boundary problem for a generalized
porous medium equation where the location of the boundary of the water mound is
determined as part of the solution. The numerical solution of the free boundary
proble... | math |
2,139 | Holistic finite differences accurately model the dynamics of the Kuramoto-Sivashinsky equation | math.NA | We analyse the nonlinear Kuramoto-Sivashinsky equation to develop an accurate
finite difference approximation to its dynamics. The analysis is based upon
centre manifold theory so we are assured that the finite difference model
accurately models the dynamics and may be constructed systematically. The
theory is applied ... | math |
2,140 | Optimal Prediction of Stiff Oscillatory Mechanics | math.NA | We consider many-body problems in classical mechanics where a wide range of
time scales limits what can be computed. We apply the method of optimal
prediction to obtain equations which are easier to solve numerically. We
demonstrate by examples that optimal prediction can reduce the amount of
computation needed to obta... | math |
2,141 | The Characteristic Length Scale of the Intermediate Structure in Zero-Pressure-Gradient Boundary Layer Flow | math.NA | In a turbulent boundary layer over a smooth flat plate with zero pressure
gradient, the intermediate structure between the viscous sublayer and the free
stream consists of two layers: one adjacent to the viscous sublayer and one
adjacent to the free stream. When the level of turbulence in the free stream is
low, the bo... | math |
2,142 | Geometrically Graded h-p Quadrature Applied to the Complex Boundary Integral Equation Method for the Dirichlet Problem with Corner Singularities | math.NA | Boundary integral methods for the solution of boundary value PDEs are an
alternative to `interior' methods, such as finite difference and finite element
methods. They are attractive on domains with corners, particularly when the
solution has singularities at these corners. In these cases, interior methods
can become ex... | math |
2,143 | Gauß Cubature for the Surface of the Unit Sphere | math.NA | Gau{\ss} cubature (multidimensional numerical integration) rules are the
natural generalisation of the 1D Gau{\ss} rules. They are optimal in the sense
that they exactly integrate polynomials of as high a degree as possible for a
particular number of points (function evaluations). For smooth integrands, they
are accura... | math |
2,144 | Partitioning Sparse Graphs using the Second Eigenvector of their Graph Laplacian | math.NA | Partitioning a graph into three pieces, with two of them large and connected,
and the third a small ``separator'' set, is useful for improving the
performance of a number of combinatorial algorithms. This is done using the
second eigenvector of a matrix defined solely in terms of the incidence matrix,
called the graph ... | math |
2,145 | A holistic finite difference approach models linear dynamics consistently | math.NA | I prove that a centre manifold approach to creating finite difference models
will consistently model linear dynamics as the grid spacing becomes small.
Using such tools of dynamical systems theory gives new assurances about the
quality of finite difference models under nonlinear and other perturbations on
grids with fi... | math |
2,146 | Irregular Input Data in Convergence Acceleration and Summation Processes: General Considerations and Some Special Gaussian Hypergeometric Series as Model Problems | math.NA | Sequence transformations accomplish an acceleration of convergence or a
summation in the case of divergence by detecting and utilizing regularities of
the elements of the sequence to be transformed. For sufficiently large indices,
certain asymptotic regularities normally do exist, but the leading elements of
a sequence... | math |
2,147 | New Numerical Algorithm for Modeling of Boson-Fermion Stars in Dilatonic Gravity | math.NA | We investigate numerically a models of the static spherically symmetric
boson-fermion stars in scalar-tensor theory of gravity with massive dilaton
field. The proper mathematical model of such stars is interpreted as a
nonlinear two-parametric eigenvalue problem with unknown internal boundary. We
employ the Continuous ... | math |
2,148 | Extrapolation Methods for Improving the Convergence of Oligomer Calculations to the Infinite Chain Limit of Quasi-Onedimensional Stereoregular Polymers | math.NA | Quasi-onedimensional stereoregular polymers as for example polyacetylene are
currently of considerable interest. There are basically two different
approaches for doing electronic structure calculations: One method is
essentially based on concepts of solid state theory. The other method is
essentially a quantum chemical... | math |
2,149 | Shock capturing by anisotropic diffusion oscillation reduction | math.NA | This paper introduces the method of anisotropic diffusion oscillation
reduction (ADOR) for shock wave computations. The connection is made between
digital image processing,in particular, image edge detection, and numerical
shock capturing. Indeed, numerical shock capturing can be formulated on the
lines of iterative di... | math |
2,150 | A Note on Regularized Shannon's Sampling Formulae | math.NA | Error estimation is given for a regularized Shannon's sampling formulae,
which was found to be accurate and robust for numerically solving partial
differential equations. | math |
2,151 | Enhanced inverse-cascade of energy in the averaged Euler equations | math.NA | For a particular choice of the smoothing kernel, it is shown that the system
of partial differential equations governing the vortex-blob method corresponds
to the averaged Euler equations. These latter equations have recently been
derived by averaging the Euler equations over Lagrangian fluctuations of length
scale $\a... | math |
2,152 | Approximation by quadrilateral finite elements | math.NA | We consider the approximation properties of finite element spaces on
quadrilateral meshes. The finite element spaces are constructed starting with a
given finite dimensional space of functions on a square reference element,
which is then transformed to a space of functions on each convex quadrilateral
element via a bil... | math |
2,153 | Gauge techniques in time and frequency domain TLM | math.NA | Typical features of the Transmission Line Matrix (TLM) algorithm in
connection with stub loading techniques and prone to be hidden in common
frequency domain formulations are elucidated within the propagator approach to
TLM. In particular, the latter reflects properly the perturbative character of
the TLM scheme and it... | math |
2,154 | Implicit integration of the TDGL equations of superconductivity | math.NA | This article is concerned with the integration of the time-dependent
Ginzburg--Landau (TDGL) equations of superconductivity. Four algorithms,
ranging from fully explicit to fully implicit, are presented and evaluated for
stability, accuracy, and compute time. The benchmark problem for the evaluation
is the equilibratio... | math |
2,155 | The frozen-field approximation and the Ginzburg-Landau equations of superconductivity | math.NA | The Ginzburg--Landau (GL) equations of superconductivity provide a
computational model for the study of magnetic flux vortices in type-II
superconductors. In this article we show through numerical examples and
rigorous mathematical analysis that the GL model reduces to the frozen-field
model when the charge of the Coop... | math |
2,156 | Discrete singular convolution and its application to computational electromagnetics | math.NA | A new computational algorithm, the discrete singular convolution (DSC), is
introduced for computational electromagnetics. The basic philosophy behind the
DSC algorithm for the approximation of functions and their derivatives is
studied. Approximations to the delta distribution are constructed as either
bandlimited repr... | math |
2,157 | Stochastic Optimal Prediction with Application to Averaged Euler Equations | math.NA | Optimal prediction (OP) methods compensate for a lack of resolution in the
numerical solution of complex problems through the use of an invariant measure
as a prior measure in the Bayesian sense. In first-order OP, unresolved
information is approximated by its conditional expectation with respect to the
invariant measu... | math |
2,158 | Conjugated filter approach for solving Burgers' equation with high Reynolds number | math.NA | We propose a conjugated filter oscillation reduction scheme for solving
Burgers' equation with high Reynolds numbers. Computational accuracy is tested
at a moderately high Reynolds number for which analytical solution is
available. Numerical results at extremely high Reynolds numbers indicate that
the proposed scheme i... | math |
2,159 | The inverse problem of the Birkhoff-Gustavson normalization and ANFER, Algorithm of Normal Form Expansion and Restoration | math.NA | In the series of papers [1-4], the inverse problem of the Birkhoff-Gustavson
normalization was posed and studied. To solve the inverse problem, the
symbolic-computing program named ANFER (Algorithm of Normal Form Expansion and
Restoration) is written up, with which a new aspect of the Bertrand and Darboux
integrability... | math |
2,160 | A backward Monte-Carlo method for solving parabolic partial differential equations | math.NA | A new Monte-Carlo method for solving linear parabolic partial differential
equations is presented. Since, in this new scheme, the particles are followed
backward in time, it provides great flexibility in choosing critical points in
phase-space at which to concentrate the launching of particles and thereby
minimizing th... | math |
2,161 | Numerical Analysis of the Non-uniform Sampling Problem | math.NA | We give an overview of recent developments in the problem of reconstructing a
band-limited signal from non-uniform sampling from a numerical analysis view
point. It is shown that the appropriate design of the finite-dimensional model
plays a key role in the numerical solution of the non-uniform sampling problem.
In the... | math |
2,162 | Non-Markovian Optimal Prediction | math.NA | Optimal prediction methods compensate for a lack of resolution in the
numerical solution of complex problems through the use of prior statistical
information. We know from previous work that in the presence of strong
underresolution a good approximation needs a non-Markovian "memory", determined
by an equation for the ... | math |
2,163 | Asymptotic Summation of Slow Converging and Rapidly Oscillating Series | math.NA | Mean values of some observables describing quantum interaction between the
Bose field in a cavity and a movable mirror can be represented as expectations
of rapidly oscillating functions w.r.t. the Poisson measure with a large mean
value ($N\approx 10^{23}$) corresponding to the average number of photons in
laser beam.... | math |
2,164 | Approximate construction of rational approximations and the effect of error autocorrection. Applications | math.NA | Several construction methods for rational approximations to functions of one
real variable are described in the present paper; the computational results
that characterize the comparative accuracy of these methods are presented; an
effect of error autocorrection is considered. This effect occurs in efficient
methods of ... | math |
2,165 | A unifying approach to software and hardware design for scientific calculations and idempotent mathematics | math.NA | A unifying approach to software and hardware design generated by ideas of
Idempotent Mathematics is discussed. The so-called idempotent correspondence
principle for algorithms, programs and hardware units is described. A software
project based on this approach is presented. | math |
2,166 | Approximate rational arithmetics and arbitrary precision computations | math.NA | We describe an approximate rational arithmetic with round-off errors (both
absolute and relative) controlled by the user. The rounding procedure is based
on the continued fraction expansion of real numbers. Results of computer
experiments are given in order to compare efficiency and accuracy of different
types of appro... | math |
2,167 | Holistic projection of initial conditions onto a finite difference approximation | math.NA | Modern dynamical systems theory has previously had little to say about finite
difference and finite element approximations of partial differential equations
(Archilla, 1998). However, recently I have shown one way that centre manifold
theory may be used to create and support the spatial discretisation of \pde{}s
such a... | math |
2,168 | Accuracy and convergence of the backward Monte-Carlo method | math.NA | The recently introduced backward Monte-Carlo method [Johan Carlsson,
arXiv:math.NA/0010118] is validated, benchmarked, and compared to the
conventional, forward Monte-Carlo method by analyzing the error in the
Monte-Carlo solutions to a simple model equation. In particular, it is shown
how the backward method reduces t... | math |
2,169 | Universal numerical algorithms and their software implementation | math.NA | The concept of a universal algorithm is discussed. Examples of this kind of
algorithms are presented. Software implementations of such algorithms in C++
type languages are discussed together with means that provide for computations
with an arbitrary accuracy. Particular emphasis is placed on universal
algorithms of lin... | math |
2,170 | On a Generalisation of Obreshkoff-Ehrlich Method for Simultaneous Extraction of All Roots of Polynomials Over an Arbitrary Chebyshev System | math.NA | New modifications of the methods for simultaneous extraction of all roots of
polynomials over an arbitrary Chebyshev system are elaborated. A cubic
convergence of iterations is proved. The method presented is a generalisation
of the classical methods of Obreshkoff and Ehrlich for simultaneous seeking of
all roots of al... | math |
2,171 | A Generalization of Obreshkoff-Ehrlich Method for Multiple Roots of Algebraic, Trigonometric and Exponential Equations | math.NA | In this paper methods for simultaneous finding all roots of generalized
polynomials are developed. These methods are related to the case when the roots
are multiple. They possess cubic rate of convergence and they are as
labour-consuming as the known methods related to the case of polynomials with
simple roots only. | math |
2,172 | Generalization of Ehrlich-Kjurkchiev method for multiple roots of algebraic equations | math.NA | In this paper a new method which is a generalization of the
Ehrlich-Kjurkchiev method is developed. The method allows to find
simultaneously all roots of the algebraic equation in the case when the roots
are supposed to be multiple with known multiplicities. The offered
generalization does not demand calculation of der... | math |
2,173 | A Generalization of Obreshkoff-Ehrlich Method for Multiple Roots of Polynomial Equations | math.NA | In this paper we develop a new method which is a generalization of the
Obreshkoff -Ehrlich method for the cases of algebraic, trigonometric and
exponential polynomials. This method has a cubic rate of convergence. It is
efficient from the computational point of view and can be used for simultaneous
finding all roots if... | math |
2,174 | Some Generalizations of the Chebyshev Method for Simultaneous Determination of All Roots of Polynomial Equations | math.NA | Iterative methods for the simultaneous determination of all roots of an
equation are dis-cussed. The multiplicities of the roots are assumed to be
known in advance. The methods are proved to have a cubical rate of convergence.
Numerical examples are given. | math |
2,175 | Eigenfunctions on a Stadium Associated with Avoided Crossings of Energy Levels | math.NA | The authors examine graphical properties of eigenfunctions with stadium
boundaries associated with avoided crossings of energy levels. | math |
2,176 | A new algorithm for the volume of a convex polytope | math.NA | We provide two algorithms for computing the volume of a convex polytope with
half-space representation {x>=0; Ax <=b} for some (m,n) matrix A and some
m-vector b. Both algorithms have a O(n^m) computational complexity which makes
them especially attractive for large n and relatively small m when the other
methods with ... | math |
2,177 | Derive boundary conditions for holistic discretisations of Burgers' equation | math.NA | I previously used Burgers' equation to introduce a new method of numerical
discretisation of \pde{}s. The analysis is based upon centre manifold theory so
we are assured that the discretisation accurately models all the processes and
their subgrid scale interactions. Here I show how boundaries to the physical
domain ma... | math |
2,178 | Solving the difference initial-boundary value problems by the operator exponential method | math.NA | We suggest a modification of the operator exponential method for the
numerical solving the difference linear initial boundary value problems. The
scheme is based on the representation of the difference operator for given
boundary conditions as the perturbation of the same operator for periodic ones.
We analyze the erro... | math |
2,179 | A Priori Estimates for the Global Error Committed by Runge-Kutta Methods for a Nonlinear Oscillator | math.NA | The Alekseev-Gr{\"o}bner lemma is combined with the theory of modified
equations to obtain an \emph{a priori} estimate for the global error of
numerical integrators. This estimate is correct up to a remainder term of order
$h^{2p}$, where $h$ denotes the step size and $p$ the order of the method. It
is applied to a cla... | math |
2,180 | Numerical Computations of Viscous, Incompressible Flow Problems Using a Two-Level Finite Element Method | math.NA | We consider two-level finite element discretization methods for the stream
function formulation of the Navier-Stokes equations. The two-level method
consists of solving a small nonlinear system on the coarse mesh, then solving a
linear system on the fine mesh. The basic result states that the errors between
the coarse ... | math |
2,181 | Direct linearization method for nonlinear PDE's and the related kernel RBFs | math.NA | The standard methodology handling nonlinear PDE's involves the two steps:
numerical discretization to get a set of nonlinear algebraic equations, and
then the application of the Newton iterative linearization or its variants to
solve the nonlinear algebraic systems. Here we present an alternative strategy
called direct... | math |
2,182 | Shock-capturing with natural high frequency oscillations | math.NA | This paper explores the potential of a newly developed conjugate filter
oscillation reduction (CFOR) scheme for shock-capturing under the influence of
natural high-frequency oscillations. The conjugate low-pass and high-pass
filters are constructed based on the principle of the discrete singular
convolution. Two Euler ... | math |
2,183 | Holistically discretise the Swift-Hohenberg equation on a scale larger than its spatial pattern | math.NA | I introduce an innovative methodology for deriving numerical models of
systems of partial differential equations which exhibit the evolution of
spatial patterns. The new approach directly produces a discretisation for the
evolution of the pattern amplitude, has the rigorous support of centre manifold
theory at finite g... | math |
2,184 | A semi-numerical computation for the added mass coefficients of an oscillating hemi-sphere at very low and very high frequencies | math.NA | A floating hemisphere under forced harmonic oscillation at very high and very
low frequencies is considered. The problem is reduced to an elliptic one, that
is, the Laplace operator in the exterior domain with standard Dirichlet and
Neumann boundary conditions, so the flow problem is simplified to standard
ones, with w... | math |
2,185 | Phase retrieval by iterated projections | math.NA | Several strategies in phase retrieval are unified by an iterative "difference
map" constructed from a pair of elementary projections and a single real
parameter $\beta$. For the standard application in optics, where the two
projections implement Fourier modulus and object support constraints
respectively, the differenc... | math |
2,186 | Bayesian Blocks in Two or More Dimensions: Image Segmentation and Cluster Analysis | math.NA | This paper describes an extension, to higher dimensions, of the Bayesian
Blocks algorithm for estimating signals in noisy time series data (Scargle
1998, 2000). The mathematical problem is to find the partition of the data
space with the maximum posterior probability for a model consisting of a
homogeneous Poisson proc... | math |
2,187 | New RBF collocation schemes and their applications | math.NA | The purpose of this study is to apply some new RBF collocation schemes and
recently-developed kernel RBFs to various types of partial differential
equation systems. By analogy with the Fasshauer's Hermite interpolation, we
recently developed the symmetric BKM and boundary particle methods (BPM), where
the latter is bas... | math |
2,188 | Detection of Edges in Spectral Data II. Nonlinear Enhancement | math.NA | We discuss a general framework for recovering edges in piecewise smooth
functions with finitely many jump discontinuities, where $[f](x):=f(x+)-f(x-)
\neq 0$. Our approach is based on two main aspects--localization using
appropriate concentration kernels and separation of scales by nonlinear
enhancement.
To detect su... | math |
2,189 | Adaptive Mollifiers for High Resolution Recovery of Piecewise Smooth Data from its Spectral Information | math.NA | We discuss the reconstruction of piecewise smooth data from its (pseudo-)
spectral information. Spectral projections enjoy superior resolution provided
the data is globally smooth, while the presence of jump discontinuities is
responsible for spurious ${\cal O}(1)$ Gibbs oscillations in the neighborhood
of edges and an... | math |
2,190 | High resolution conjugate filters for the simulation of flows | math.NA | This paper proposes a Hermite-kernel realization of the conjugate filter
oscillation reduction (CFOR) scheme for the simulation of fluid flows. The
Hermite kernel is constructed by using the discrete singular convolution (DSC)
algorithm, which provides a systematic generation of low-pass filter and its
conjugate high-p... | math |
2,191 | Shape reconstruction in scattering media with voids using a transport model and level sets | math.NA | A two-step shape reconstruction method for diffuse optical tomography (DOT)
is presented which uses adjoint fields and level sets. The propagation of
near-infrared photons in tissue is modeled by the time-dependent linear
transport equation, of which the absorption parameter has to be reconstructed
from boundary measur... | math |
2,192 | Finite volume methods for incompressible flow | math.NA | Two finite volume methods are derived and applied to the solution of problems
of incompressible flow. In particular, external inviscid flows and
boundary-layer flows are examined. The firstmethod analyzed is a cell-centered
finite volume scheme. It is shown to be formally first order accurate on
equilateral triangles a... | math |
2,193 | Double newtonisation of fixed point sequences | math.NA | A neutral fixed point of a real iteration map $u$ becomes a super attracting
fixed point using a suitable double newtonisation. The map $u$ is so
transformed into a map $w$ which is here called the standard accelerator of
$u$. The map $w$ provides a unifying process to deal with a large set of fixed
point sequences whi... | math |
2,194 | New Method to obtain Exact-Fit Polynomial and Exponential | math.NA | The existing methods to obtain an exact-fit polynomial does not give the
resulting polynomial in its standard form, and further manipulations are needed
to obtain that. The new method presented here gives the coefficients of the
polynomial in the standard form directly. It is also possible to obtain the
exact-fit expon... | math |
2,195 | Algorithm to generate ideals in a Lie algebra of matrices at any particular characteristic with Mathematica | math.NA | We present in this paper a routine which construct the ideal generated by a
list of elements in a matrix Lie algebra at any particular characteristic. We
have used this algorithm to analyze the problem of the simplicity of some Lie
algebras. | math |
2,196 | Algorithm to compute the rank and a Cartan subalgebra of a matrix Lie algebra with Mathematica | math.NA | We present in this paper a set of routines constructed to compute the rank of
a matrix Lie algebra and also to determine a Cartan subalgebra from a given
list of elements | math |
2,197 | Large Eddy Simulation of Turbulent Channel Flows by the Rational LES Model | math.NA | The rational large eddy simulation (RLES) model is applied to turbulent
channel flows. This approximate deconvolution model is based on a rational
(subdiagonal Pade') approximation of the Fourier transform of the Gaussian
filter and is proposed as an alternative to the gradient (also known as the
nonlinear or tensor-di... | math |
2,198 | The Lie algebra splitg2 with Mathematica using Zorn's matrices | math.NA | We will obtain in this paper a generic expression of any element in athe Lie
algebra of the derivations of the split octonions a over an arbitrary field.
For this purpose, we will use the Zorn's matrices. We will also compute the
multiplication table of this Lie algebra. | math |
2,199 | About Calculation of the Hankel Transform Using Preliminary Wavelet Transform | math.NA | The purpose of this paper is to present an algorithm for evaluating Hankel
transform of the null and the first kind. The result is the exact analytical
representation as the series of the Bessel and Struve functions multiplied by
the wavelet coefficients of the input function. Numerical evaluation of the
test function ... | math |
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