
LAPACK
 Referenced in 1504 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 1241 articles
[sw04827]
 functions for constructing test matrices, computing matrix factorizations, visualizing matrices, and carrying out direct search...

SINGULAR
 Referenced in 1195 articles
[sw00866]
 Tangent Cone algorithm. Furthermore, it provides polynomial factorizations, resultant, characteristic set and gcd computations, syzygy...

ARPACK
 Referenced in 727 articles
[sw04218]
 problems. For many standard problems, a matrix factorization is not required. Only the action...

REDUCE
 Referenced in 709 articles
[sw00789]
 extending program syntax; analytic differentiation and integration; factorization of polynomials; facilities for the solution...

CoCoA
 Referenced in 564 articles
[sw00143]
 dimensional schemes, Poincare’ series and Hilbert functions, factorization of polynomials, toric ideals. The capabilities...

ScaLAPACK
 Referenced in 377 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...

UMFPACK
 Referenced in 277 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...

MINOS
 Referenced in 432 articles
[sw05095]
 basis package (for maintaining sparse LU factors of the basis matrix), automatic scaling of linear...

MUMPS
 Referenced in 309 articles
[sw04013]
 unsymmetric matrices; Version for complex arithmetic; Parallel factorization and solve phases (uniprocessor version also available ... format; distributed assembled format; elemental format; Partial factorization and Schur complement matrix (centralized...

symrcm
 Referenced in 328 articles
[sw08566]
 good preordering for LU or Cholesky factorization of matrices that come from long, skinny problems...

CGS
 Referenced in 289 articles
[sw08225]
 preconditioning called ILLU (an incomplete lineLUfactorization). The conclusion of the author is that...

WEKA
 Referenced in 239 articles
[sw06435]
 This article provides an overview of the factors that we believe to be important...

ILUT
 Referenced in 124 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...

SuperLU
 Referenced in 138 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 147 articles
[sw02791]
 critical components in a GRG code: basis factorizations, search directions, linesearches, and Newton iterations...

TensorToolbox
 Referenced in 87 articles
[sw04185]
 Efficient MATLAB computations with sparse and factored tensors. The term tensor refers simply ... tensor decomposition algorithms. Second, we study factored tensors, which have the property that they ... which itself may be dense, sparse, or factored) and a matrix along each mode...

CHOLMOD
 Referenced in 78 articles
[sw04412]
 Algorithm 887: CHOLMOD, Supernodal Sparse Cholesky Factorization and Update/Downdate. CHOLMOD is a set of routines ... factorizing sparse symmetric positive definite matrices of the form A or AAT, updating/downdating a sparse ... Cholesky factorization, solving linear systems, updating/downdating the solution to the triangular system ... symmetric and unsymmetric matrices. Its supernodal Cholesky factorization relies on LAPACK and the Level...

SDPLR
 Referenced in 96 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...