• UMFPACK

  • Referenced in 325 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...
  • MINOS

  • Referenced in 440 articles [sw05095]
  • basis package (for maintaining sparse LU factors of the basis matrix), automatic scaling of linear...
  • LAPACK

  • Referenced in 1582 articles [sw00503]
  • singular value problems. The associated matrix factorizations (LU, Cholesky, QR, SVD, Schur, generalized Schur ... factorizations and estimating condition numbers. Dense and banded matrices are handled, but not general sparse ... reorganizing the algorithms to use block matrix operations, such as matrix multiplication, in the innermost...
  • TensorToolbox

  • Referenced in 121 articles [sw04185]
  • itself may be dense, sparse, or factored) and a matrix along each mode...
  • CHOLMOD

  • Referenced in 88 articles [sw04412]
  • updating/downdating a sparse Cholesky factorization, solving linear systems, updating/downdating the solution to the triangular system ... other sparse matrix functions for both symmetric and unsymmetric matrices. Its supernodal Cholesky factorization relies ... sparse symmetric positive definite, as well as in several other sparse matrix functions...
  • symrcm

  • Referenced in 374 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...
  • DSPCA

  • Referenced in 35 articles [sw04804]
  • decomposition of a covariance matrix into sparse factors, and has wide applications ranging from biology ... largest eigenvalue of a symmetric matrix, where cardinality is constrained, and derive a semidefinite programming ... arising in the direct sparse PCA method...
  • ARPACK

  • Referenced in 770 articles [sw04218]
  • large sparse or structured matrices A where structured means that a matrix-vector product ... Implicitly Restarted Arnoldi Method (IRAM). When the matrix A is symmetric it reduces ... problems. For many standard problems, a matrix factorization is not required. Only the action...
  • TNPACK

  • Referenced in 39 articles [sw00970]
  • sparse modified Cholesky factorization based on the Yale Sparse Matrix Package. In this paper...
  • Amesos2

  • Referenced in 9 articles [sw18349]
  • common interface to many different sparse matrix factorization codes, and can handle any implementation...
  • Tensorlab

  • Referenced in 44 articles [sw14255]
  • coupled) matrix and tensor factorizations with structured factors and support for dense, sparse and incomplete...
  • SuperLU

  • Referenced in 162 articles [sw00930]
  • library for the direct solution of large, sparse, nonsymmetric systems of linear equations on high ... through forward and back substitution. The LU factorization routines can handle non-square matrices ... performed only for square matrices. The matrix columns may be preordered (before factorization) either through...
  • SPARSE-QR

  • Referenced in 17 articles [sw05215]
  • Sparse QR factorization in MATLAB In the recently presented sparse matrix extension of MATLAB, there...
  • SQOPT

  • Referenced in 17 articles [sw07860]
  • basis package (for maintaining sparse LU factors of the basis matrix), a practical anti-degeneracy...
  • COLAMD

  • Referenced in 28 articles [sw00145]
  • prior to numerical factorization, and (2) sparse Cholesky factorization, which requires a symmetric permutation ... rows and columns of the matrix being factorized. These orderings are computed by COLAMD ... ordering from COLAMD is also suitable for sparse QR factorization, and the factorization of matrices...
  • SuiteSparseQR

  • Referenced in 27 articles [sw07348]
  • sparse QR factorization package based on the multifrontal method. Within each frontal matrix, LAPACK ... eliminates singletons by permuting the input matrix A into the form ... reducing ordering, column elimination tree, and frontal matrix structures are found without requiring the formation ... sufficiently large problems, the resulting sparse QR factorization obtains a substantial fraction of the theoretical...
  • MA57

  • Referenced in 83 articles [sw00536]
  • code for the direct solution of sparse symmetric linear equations that solves indefinite systems with ... These include restart facilities, matrix modification, partial solution for matrix factors, solution of multiple right...
  • TAUCS

  • Referenced in 30 articles [sw04014]
  • than the supernodal solvers when it factors a matrix completely, but it can drop small ... systems. Out-of-Core Sparse LU with Partial Pivoting Factor and Solve. Can solve huge ... symmetric orderings. Matrix Operations. Matrix-vector multiplication, triangular solvers, matrix reordering. Matrix Input/Output. Routines ... dropping nonzeros from the coefficient matrix and them factoring the preconditioner directly. Recursive Vaidya...
  • LIPSOL

  • Referenced in 79 articles [sw04712]
  • large problems. It utilizes Matlab’s sparse-matrix data-structure and Application Program Interface facility ... existing, efficient Fortran codes for solving large, sparse, symmetric positive definite linear systems. Specifically, LIPSOL ... files from two Fortran packages: a sparse Cholesky factorization package developed by Esmond...
  • ILUM

  • Referenced in 61 articles [sw07244]
  • general sparse matrices Standard preconditioning techniques based on incomplete LU (ILU) factorizations offer a limited ... applying the usual ILU factorization to a matrix obtained from a multicolor ordering.par We present ... ILUs based on threshold techniques. The ILUM factorization described in this paper is in this ... methods that deal specifically with general unstructured sparse matrices such as those arising from finite...