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id stringlengths 40 40	title stringlengths 15 120	text stringlengths 41 3.14k	source stringclasses 2 values
a5df45567a1db81a2301eeaec12e65bb2c559119	numerical linear algebra, sometimes called applied linear algebra,	numerical linear algebra, sometimes called applied linear algebra, is the study of how matrix operations can be used to create computer algorithms which efficiently and accurately provide approximate answers to questions in continuous mathematics. it is a subfield of numerical analysis, and a type of linear algebra. co...	wikipedia
c7db6ddd733800ca4a76d72b85d474e31de76579	several programming languages use numerical linear algebra optimisation	several programming languages use numerical linear algebra optimisation techniques and are designed to implement numerical linear algebra algorithms. these languages include matlab, analytica, maple, and mathematica. other programming languages which are not explicitly designed for numerical linear algebra have librari...	wikipedia
ab33831589c28e44b959d899130b64bb3768f722	the core of many iterative methods in numerical	the core of many iterative methods in numerical linear algebra is the projection of a matrix onto a lower dimensional krylov subspace, which allows features of a high-dimensional matrix to be approximated by iteratively computing the equivalent features of similar matrices starting in a low dimension space and moving t...	wikipedia
0aacb0dd8efcb890849671b3b1609518b08fc510	there are two reasons that iterative algorithms are	there are two reasons that iterative algorithms are an important part of numerical linear algebra. first, many important numerical problems have no direct solution; in order to find the eigenvalues and eigenvectors of an arbitrary matrix, we can only adopt an iterative approach. second, noniterative algorithms for an a...	wikipedia
4d230bd29c93d4af8eda1c16196a5068e52b1384	instability is the tendency of computer algorithms, which	instability is the tendency of computer algorithms, which depend on floating-point arithmetic, to produce results that differ dramatically from the exact mathematical solution to a problem. when a matrix contains real data with many significant digits, many algorithms for solving problems like linear systems of equatio...	wikipedia
5e7c030e7936ff02d91ea04724b289f0f431f29d	allow that a problem is a function f:	allow that a problem is a function f: x → y {\displaystyle f:x\to y}, where x is a normed vector space of data and y is a normed vector space of solutions. for some data point x ∈ x {\displaystyle x\in x}, the problem is said to be ill-conditioned if a small perturbation in x produces a large change in the value of f (...	wikipedia
af0f4241c4bc344c97063a16ffa9bcc87c85d21a	matrix decompositions suggest a number of ways to	matrix decompositions suggest a number of ways to solve the linear system r = b − ax where we seek to minimize r, as in the regression problem. the qr algorithm solves this problem by computing the reduced qr factorization of a and rearranging to obtain r ^ x = q ^ ∗ b {\displaystyle {\widehat {r}}x={\widehat {q}}^{\as...	wikipedia
8f65bffb34a244dde08645d9dc05e2bd98c7bcf4	many different decompositions can be used to solve	many different decompositions can be used to solve the linear problem, depending on the characteristics of the matrix a and the vectors x and b, which may make one factorization much easier to obtain than others. if a = qr is a qr factorization of a, then equivalently r x = q ∗ b {\displaystyle rx=q^{\ast }b}. this is ...	wikipedia
5f17d781301e1afe4c65a5b18633bc4cbdba615f	numerical linear algebra characteristically approaches matrices as a	numerical linear algebra characteristically approaches matrices as a concatenation of columns vectors. in order to solve the linear system x = a − 1 b {\displaystyle x=a^{-1}b}, the traditional algebraic approach is to understand x as the product of a − 1 {\displaystyle a^{-1}} with b. numerical linear algebra instead ...	wikipedia
c4a5d796531bfed83d60d23d49c9b7266f5cd051	from the numerical linear algebra perspective, gaussian elimination	from the numerical linear algebra perspective, gaussian elimination is a procedure for factoring a matrix a into its lu factorization, which gaussian elimination accomplishes by left-multiplying a by a succession of matrices l m − 1 ⋯ l 2 l 1 a = u {\displaystyle l_{m-1}\cdots l_{2}l_{1}a=u} until u is upper triangular...	wikipedia
f800e7190deac0887c8729d0cf89a0830c9a0191	the eigenvalue decomposition of a matrix a m	the eigenvalue decomposition of a matrix a m × m {\displaystyle a^{m\times m}} is a = x Λ x − 1 {\displaystyle a=x\lambda x^{-1}}, where the columns of x are the eigenvectors of a, and Λ {\displaystyle \lambda } is a diagonal matrix the diagonal entries of which are the corresponding eigenvalues of a. there is no direc...	wikipedia
76313c5b443e73e8379f3bd054723a065a3dbfa5	an lu factorization of a matrix a consists	an lu factorization of a matrix a consists of a lower triangular matrix l and an upper triangular matrix u so that a = lu. the matrix u is found by an upper triangularization procedure which involves left-multiplying a by a series of matrices m 1, …, m n − 1 {\displaystyle m_{1},\ldots,m_{n-1}} to form the product m n ...	wikipedia
1cbe073b4d9da3dd9de930596499c72ae6014c50	the qr factorization of a matrix a m	the qr factorization of a matrix a m × n {\displaystyle a^{m\times n}} is a matrix q m × m {\displaystyle q^{m\times m}} and a matrix r m × n {\displaystyle r^{m\times n}} so that a = qr, where q is orthogonal and r is upper triangular. the two main algorithms for computing qr factorizations are the gram–schmidt proces...	wikipedia
8e4d3dec0bb959aa5f4618372f6c84cbfdd81341	the singular value decomposition of a matrix a	the singular value decomposition of a matrix a m × n {\displaystyle a^{m\times n}} is a = u Σ v ∗ {\displaystyle a=u\sigma v^{\ast }} where u and v are unitary, and Σ {\displaystyle \sigma } is diagonal. the diagonal entries of Σ {\displaystyle \sigma } are called the singular values of a. because singular values are t...	wikipedia
9ce950e1217bfdf9b358e3b7cd97b3b51d0718f1	for many problems in applied linear algebra, it	for many problems in applied linear algebra, it is useful to adopt the perspective of a matrix as being a concatenation of column vectors. for example, when solving the linear system x = a − 1 b {\displaystyle x=a^{-1}b}, rather than understanding x as the product of a − 1 {\displaystyle a^{-1}} with b, it is helpful t...	wikipedia
7eb5cae4eea9c16894b966715ed4bffc2d63f0f8	numerical linear algebra was developed by computer pioneers	numerical linear algebra was developed by computer pioneers like john von neumann, alan turing, james h. wilkinson, alston scott householder, george forsythe, and heinz rutishauser, in order to apply the earliest computers to problems in continuous mathematics, such as ballistics problems and the solutions to systems o...	wikipedia
57dc5daeeb6be9d841e73fed5033aef8c719ef10	common problems in numerical linear algebra include obtaining	common problems in numerical linear algebra include obtaining matrix decompositions like the singular value decomposition, the qr factorization, the lu factorization, or the eigendecomposition, which can then be used to answer common linear algebraic problems like solving linear systems of equations, locating eigenvalu...	wikipedia
bb7f9c23e132abc6499f2e86654a3c5b5c69f40b	numerical linear algebra aims to solve problems of	numerical linear algebra aims to solve problems of continuous mathematics using finite precision computers, so its applications to the natural and social sciences are as vast as the applications of continuous mathematics. it is often a fundamental part of engineering and computational science problems, such as image an...	wikipedia
f5d34ec80847b1d9d5ffb60bcf60ed2fa59971c9	numerical linear algebra, sometimes called applied linear algebra,	numerical linear algebra, sometimes called applied linear algebra, is the study of how matrix operations can be used to create computer algorithms which efficiently and accurately provide approximate answers to questions in continuous mathematics. it is a subfield of numerical analysis, and a type of linear algebra. co...	wikipedia
51d360a1b8b9b691aea03baa9c9c91d0506daa87	the 2012–13 g4s korvpalli meistriliiga was the 88th	the 2012–13 g4s korvpalli meistriliiga was the 88th season of the estonian basketball league and the fourth under the title sponsorship of g4s. kalev/cramo came into the season as defending champions of the 2011–12 kml season. the season started on 10 october 2012 and concluded on 17 may 2013 with kalev/cramo defeating...	wikipedia
fc5b339fca3385e5e14edeb244042ac8ce0bc866	the season started on 10 october 2012 and	the season started on 10 october 2012 and concluded on 17 may 2013 with kalev/cramo defeating tÜ/rock 4 games to 0 in the finals to win their 6th estonian league title.	wikipedia
cac02747e9e4e7a84e3c9c0f1abf1b037b47a1f9	the 2012–13 g4s korvpalli meistriliiga was the 88th	the 2012–13 g4s korvpalli meistriliiga was the 88th season of the estonian basketball league and the fourth under the title sponsorship of g4s. kalev/cramo came into the season as defending champions of the 2011–12 kml season.	wikipedia
605918f8c51ebb3c98b23ca8f143fb0857da76e2	the parklinks bridge is a structure which crosses	the parklinks bridge is a structure which crosses over the marikina river connecting the cities of pasig and quezon city. it is part of the parklinks mixed-use development of ayala land and eton properties. the road bridge spans 110 m (360 ft) and has a width of 25 m (82 ft). imitating a cable-stayed bridge, parklinks ...	wikipedia
882c1c111b60c2379f688ddd56b7edca32489066	the marietta–williamstown interstate bridge is a four-lane truss	the marietta–williamstown interstate bridge is a four-lane truss bridge carries interstate 77 between williamstown, west virginia and marietta, ohio. the bridge was completed in 1967 and it was rehabilitated in 2003.	wikipedia
d9b1a8cba2aeedbefb3afb2402e5292c806bc39b	the marietta – williamstown interstate bridge is a	the marietta – williamstown interstate bridge is a four-lane truss bridge carries interstate 77 between williamstown, west virginia and marietta, ohio. the bridge was completed in 1967 and it was rehabilitated in 2003.	wikipedia
3ad9a6dede4d4d449fbd0261165b8f3e858a6457	the 1987 1000 km jerez was the second	the 1987 1000 km jerez was the second round of the 1987 world sports-prototype championship. it took place at the circuito permanente de jerez, spain on march 29, 1987.	wikipedia
75a8f2c6446cccc9ad93e8a748b14bc370c30229	michael john hudak is an environmental researcher and	michael john hudak is an environmental researcher and author, sierra club activist, radio broadcaster, and public speaker concerned with the environmental damage that ranching inflicts on us public land. he is an author of western turf wars: the politics of public lands ranching and its companion series of web-based vi...	wikipedia
6d3502d6458442b3dc69bc27503b04fb2e2019c5	while gathering signatures on the ballot petition, he	while gathering signatures on the ballot petition, he chaired a sierra club subcommittee advocating adoption of conservation policy to end commercial livestock grazing on federal public lands. these negotiations at the september 2000 board meeting led to the grazing policy adopted by the club's board of directors at th...	wikipedia
d0e38d48994c73c6a32baed7194f262b40f0dab5	as resource person to the sierra club 's	as resource person to the sierra club 's grazing task force from june 1999 to may 2000, he learned in december 1999 that the club's national board planned to consider revising that policy at its may 2000 meeting. when the board in early may postpone that discussion until its september meeting, he began qualifying a mem...	wikipedia
60998203f193af9c2affe92db56dba42ad4bd05d	in 1997, after several years of hiking on	in 1997, after several years of hiking on western public lands during which he noted livestock impacts, he began a more intensive study of livestock production by researching publications and traveling across the west for more than twenty months. between february 1998 and may 2000, he presented forty-five photographic ...	wikipedia
2c438598555a4e12f753e7eb08e490b842f177e2	from 1993 to 1994, he served as the	from 1993 to 1994, he served as the binghamton (ny) regional coordinator for the short-lived beyond beef campaign (headed by jeremy rifkin and howard lyman), which mobilized grassroots support in favor of mcdonald's offering a meatless (vegetarian) eco-burger at all its north american outlets.	wikipedia
5698b47dad20bcd0a2a483bfdaa83f47e0c56149	before he focused entirely upon environmental activism and	before he focused entirely upon environmental activism and advocacy, he was a computer industry researcher. his doctorate (1986) in advanced technology (computer science) and bachelor's degree (mathematics) (1975) are from binghamton university (also known as state university of new york at binghamton), and his master'...	wikipedia
9e8fcd9e9e377833989dd763354d5471a1d79f84	michael john hudak is an environmental researcher and	michael john hudak is an environmental researcher and author, sierra club activist, radio broadcaster, and public speaker concerned with the environmental damage (and harm to free-living animals, or wildlife) that ranching inflicts on us public land (mostly in the western states). he is an author of western turf wars: ...	wikipedia
2724bb268dd1b210b4b2d5b303025496635ffcb9	the 2011–12 season will be sc bastia's first	the 2011–12 season will be sc bastia's first season back in ligue 2 since promotion from championnat national in 2011. ranked first in the league this season and promoted to ligue 1. while the cup "last 32" round is struggling. more died in the first round of the league cup. bastia, newly promoted from the national, we...	wikipedia
166179ab935e9c2d726329380ba57c75962c72c5	kappa manufacrounded the kits for bastia. oscaro remained	kappa manufacrounded the kits for bastia. oscaro remained as the club's main sponsor. was backpack sponsor; géant, sponsor of the arm; haute-corse conseil general, shorts sponsor; corsica ferries. in jerseys, introduced on 27 june 2011.	wikipedia
461b1abb71dfe0935c269a34e4bdeb78bba7f150	bastia won all the trophies unfp for ligue	bastia won all the trophies unfp for ligue 2. jérôme rothen, best player, macedo novaes, best goalkeeper, and frédéric hantz, best coach, who placed five players in the team lineup (macedo novaes, féthi harek, wahbi khazri, sadio diallo and jérôme rothen).	wikipedia
4dee9e72725ee642c65f6bf1037788e600d8387b	bastia, newly promoted from the national, welcomed jérôme	bastia, newly promoted from the national, welcomed jérôme rothen, toifilou maoulida, françois marque, ludovic genest and florian thauvin into the club. bastia started off on a good note, falling off slightly in the autumn. from early february until the beginning of april, bastia did not lose a single match. on 23 april...	wikipedia
c00ce312368704a20bafb8641453471865cdd8eb	the 2011–12 season will be sc bastia '	the 2011–12 season will be sc bastia ' s first season back in ligue 2 since promotion from championnat national in 2011. ranked first in the league this season and promoted to ligue 1. while the cup "last 32" round is struggling. more died in the first round of the league cup.	wikipedia
9665ad8d81fb0e47f02616afb96a6fbde4119dfb	pankaj kumar agarwal is an indian computer scientist	pankaj kumar agarwal is an indian computer scientist and mathematician researching algorithms in computational geometry and related areas. he is the rjr nabisco professor of computer science and mathematics at duke university, where he has been chair of the computer science department since 2004. he obtained his doctor...	wikipedia
2ecf6fdcc6114ebea20b7f315e6caef33f39a4fb	agarwal was elected as a fellow of the	agarwal was elected as a fellow of the association for computing machinery in 2002. he is also former duke bass fellow and an alfred p. sloan fellow. he was the recipient of a national young investigator award in 1993. before holding the rjr nabisco professorship, he was the earl d. mclean jr. professor of computer sci...	wikipedia