
LAPACK
 Referenced in 1626 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 ... reorganizing the algorithms to use block matrix operations, such as matrix multiplication, in the innermost...

mctoolbox
 Referenced in 1391 articles
[sw04827]
 functions for constructing test matrices, computing matrix factorizations, visualizing matrices, and carrying out direct search ... toolbox supersedes the author’s earlier Test Matrix Toolbox (final release 1995). The toolbox...

ARPACK
 Referenced in 783 articles
[sw04218]
 problems. For many standard problems, a matrix factorization is not required. Only the action...

ScaLAPACK
 Referenced in 404 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 ... solvers for LU, Cholesky, and QR, the matrix sign function for eigenproblems...

UMFPACK
 Referenced in 354 articles
[sw00989]
 ordering and analyzing a sparse matrix, computing the numerical factorization, solving a system with ... factors, transposing and permuting a sparse matrix, and converting between sparse matrix representations.\parThe simple ... from the details of the complex sparse factorization data structures by returning simple handles...

MUMPS
 Referenced in 422 articles
[sw04013]
 unsymmetric matrices; Version for complex arithmetic; Parallel factorization and solve phases (uniprocessor version also available ... Iterative refinement and backward error analysis; Various matrix input formats assembled format; distributed ... assembled format; elemental format; Partial factorization and Schur complement matrix (centralized or 2D blockcyclic...

MINOS
 Referenced in 441 articles
[sw05095]
 package (for maintaining sparse LU factors of the basis matrix), automatic scaling of linear contraints...

MA57
 Referenced in 86 articles
[sw00536]
 facilities, matrix modification, partial solution for matrix factors, solution of multiple righthand sides...

TensorToolbox
 Referenced in 139 articles
[sw04185]
 dense, sparse, or factored) and a matrix along each mode, and a Kruskal tensor...

SuperLU
 Referenced in 171 articles
[sw00930]
 through forward and back substitution. The LU factorization routines can handle nonsquare matrices ... square matrices. The matrix columns may be preordered (before factorization) either through library or user...

NeNMF
 Referenced in 30 articles
[sw17586]
 optimal gradient method for nonnegative matrix factorization. Nonnegative matrix factorization (NMF) is a powerful ... product of two lowrank nonnegative matrix factors. It has been widely applied to signal ... particular, at each iteration round, the matrix factor is updated by using the PG method ... optimally at rate in optimizing each matrix factor, it is superior...

TRICE
 Referenced in 46 articles
[sw05197]
 particular they do not rely on matrix factorizations of the linearized constraints but use solutions...

REDUCE
 Referenced in 739 articles
[sw00789]
 extending program syntax; analytic differentiation and integration; factorization of polynomials; facilities for the solution ... wide variety of special functions; Dirac matrix calculations of interest to high energy physicists...

TAUCS
 Referenced in 31 articles
[sw04014]
 than the supernodal solvers when it factors a matrix completely, but it can drop small ... Core Sparse LU with Partial Pivoting Factor and Solve. Can solve huge unsymmetric linear systems ... dropping nonzeros from the coefficient matrix and them factoring the preconditioner directly. Recursive Vaidya ... nonzeros, but they don’t factor the resulting matrix completely. Instead, they eliminate rows...

ILUM
 Referenced in 62 articles
[sw07244]
 applying the usual ILU factorization to a matrix obtained from a multicolor ordering.par We present...

GPCRCA
 Referenced in 35 articles
[sw25949]
 Meanwhile, the graylevel cooccurrence matrix factors extracted from the CA images are used...

CHOLMOD
 Referenced in 95 articles
[sw04412]
 updating/downdating a sparse Cholesky factorization, solving linear systems, updating/downdating the solution to the triangular system ... sparse matrix functions for both symmetric and unsymmetric matrices. Its supernodal Cholesky factorization relies ... well as in several other sparse matrix functions...

symrcm
 Referenced in 376 articles
[sw08566]
 good preordering for LU or Cholesky factorization of matrices that come from long, skinny problems ... nonsymmetric S. For a real, symmetric sparse matrix, S, the eigenvalues...

SuperLUDIST
 Referenced in 83 articles
[sw00002]
 through forward and back substitution. The LU factorization routines can handle nonsquare matrices ... square matrices. The matrix columns may be preordered (before factorization) either through library or user...

LowRankModels
 Referenced in 24 articles
[sw27002]
 matrix completion, robust PCA, nonnegative matrix factorization, kmeans, and many more. For more information...