
LAPACK
 Referenced in 1181 articles
[sw00503]
 singular value problems. The associated matrix factorizations (LU, Cholesky, QR, SVD, Schur, generalized Schur ... computations such as reordering of the Schur factorizations and estimating condition numbers. Dense and banded...

mctoolbox
 Referenced in 1009 articles
[sw04827]
 functions for constructing test matrices, computing matrix factorizations, visualizing matrices, and carrying out direct search...

SINGULAR
 Referenced in 922 articles
[sw00866]
 Tangent Cone algorithm. Furthermore, it provides polynomial factorizations, resultant, characteristic set and gcd computations, syzygy...

REDUCE
 Referenced in 635 articles
[sw00789]
 extending program syntax; analytic differentiation and integration; factorization of polynomials; facilities for the solution...

ARPACK
 Referenced in 583 articles
[sw04218]
 problems. For many standard problems, a matrix factorization is not required. Only the action...

CoCoA
 Referenced in 476 articles
[sw00143]
 dimensional schemes, Poincare’ series and Hilbert functions, factorization of polynomials, toric ideals. The capabilities...

ScaLAPACK
 Referenced in 319 articles
[sw00830]
 iterative refinement, for LU and Cholesky factorization, matrix inversion, fullrank linear least squares problems ... orthogonal and generalized orthogonal factorizations, orthogonal transformation routines, reductions to upper Hessenberg, bidiagonal and tridiagonal...

MINOS
 Referenced in 409 articles
[sw05095]
 basis package (for maintaining sparse LU factors of the basis matrix), automatic scaling of linear...

UMFPACK
 Referenced in 180 articles
[sw00989]
 ANSI C code for sparse LU factorization is presented that combines a column preordering ... rightlooking unsymmetricpattern multifrontal numerical factorization. The preordering and symbolic analysis phase computes ... memory usage during the subsequent numerical factorization. Usercallable routines are provided for ordering ... analyzing a sparse matrix, computing the numerical factorization, solving a system with the LU factors...

CGS
 Referenced in 269 articles
[sw08225]
 preconditioning called ILLU (an incomplete lineLUfactorization). The conclusion of the author is that...

symrcm
 Referenced in 227 articles
[sw08566]
 good preordering for LU or Cholesky factorization of matrices that come from long, skinny problems...

ILUT
 Referenced in 84 articles
[sw08734]
 ILUT: A dual threshold incomplete LU factorization. In this paper we describe an Incomplete ... factorization technique based on a strategy which combines two heuristics. This ILUT factorization extends ... usual ILU(O) factorization without using the concept of level of fillin. There ... traditional ways of developing incomplete factorization preconditioners. The first uses a symbolic factorization approach...

WEKA
 Referenced in 143 articles
[sw06435]
 This article provides an overview of the factors that we believe to be important...

SuperLU
 Referenced in 88 articles
[sw00930]
 through forward and back substitution. The LU factorization routines can handle nonsquare matrices ... matrix columns may be preordered (before factorization) either through library or user supplied routines. This ... sparsity is completely separate from the factorization. Working precision iterative refinement subroutines are provided...

CONOPT
 Referenced in 116 articles
[sw02791]
 critical components in a GRG code: basis factorizations, search directions, linesearches, and Newton iterations...

SDPLR
 Referenced in 82 articles
[sw04745]
 based on the idea of lowrank factorization. A specialized version of SDPLR is also ... Algorithm for Semidefinite Programs via Lowrank Factorization” written by S. Burer and R.D.C. Monteiro...

ILUM
 Referenced in 57 articles
[sw07244]
 preconditioning techniques based on incomplete LU (ILU) factorizations offer a limited degree of parallelism ... polynomial precoditioning or applying the usual ILU factorization to a matrix obtained from a multicolor ... ordering.par We present an incomplete factorization technique based on independent set orderings and multicoloring ... ILUs based on threshold techniques. The ILUM factorization described in this paper is in this...

SuperLUDIST
 Referenced in 59 articles
[sw00002]
 through forward and back substitution. The LU factorization routines can handle nonsquare matrices ... matrix columns may be preordered (before factorization) either through library or user supplied routines. This ... sparsity is completely separate from the factorization. Working precision iterative refinement subroutines are provided...

DEVEX
 Referenced in 94 articles
[sw08378]
 process, the author introduces dynamic column weighting factors as a means of estimating gradients...