• LAPACK

  • Referenced in 1471 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 1219 articles [sw04827]
  • functions for constructing test matrices, computing matrix factorizations, visualizing matrices, and carrying out direct search...
  • SINGULAR

  • Referenced in 1165 articles [sw00866]
  • Tangent Cone algorithm. Furthermore, it provides polynomial factorizations, resultant, characteristic set and gcd computations, syzygy...
  • ARPACK

  • Referenced in 712 articles [sw04218]
  • problems. For many standard problems, a matrix factorization is not required. Only the action...
  • REDUCE

  • Referenced in 703 articles [sw00789]
  • extending program syntax; analytic differentiation and integration; factorization of polynomials; facilities for the solution...
  • CoCoA

  • Referenced in 556 articles [sw00143]
  • dimensional schemes, Poincare’ series and Hilbert functions, factorization of polynomials, toric ideals. The capabilities...
  • ScaLAPACK

  • Referenced in 375 articles [sw00830]
  • iterative refinement, for LU and Cholesky factorization, matrix inversion, full-rank linear least squares problems ... orthogonal and generalized orthogonal factorizations, orthogonal transformation routines, reductions to upper Hessenberg, bidiagonal and tridiagonal...
  • UMFPACK

  • Referenced in 269 articles [sw00989]
  • ANSI C code for sparse LU factorization is presented that combines a column pre-ordering ... right-looking unsymmetric-pattern multifrontal numerical factorization. The pre-ordering and symbolic analysis phase computes ... memory usage during the subsequent numerical factorization. User-callable routines are provided for ordering ... analyzing a sparse matrix, computing the numerical factorization, solving a system with the LU factors...
  • MINOS

  • Referenced in 431 articles [sw05095]
  • basis package (for maintaining sparse LU factors of the basis matrix), automatic scaling of linear...
  • MUMPS

  • Referenced in 298 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 326 articles [sw08566]
  • good preordering for LU or Cholesky factorization of matrices that come from long, skinny problems...
  • CGS

  • Referenced in 288 articles [sw08225]
  • preconditioning called ILLU (an incomplete line-LU-factorization). The conclusion of the author is that...
  • WEKA

  • Referenced in 229 articles [sw06435]
  • This article provides an overview of the factors that we believe to be important...
  • ILUT

  • Referenced in 120 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 fill-in. There ... traditional ways of developing incomplete factorization preconditioners. The first uses a symbolic factorization approach...
  • SuperLU

  • Referenced in 135 articles [sw00930]
  • through forward and back substitution. The LU factorization routines can handle non-square 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 145 articles [sw02791]
  • critical components in a GRG code: basis factorizations, search directions, line-searches, and Newton iterations...
  • SDPLR

  • Referenced in 95 articles [sw04745]
  • based on the idea of low-rank factorization. A specialized version of SDPLR is also ... Algorithm for Semidefinite Programs via Low-rank Factorization” written by S. Burer and R.D.C. Monteiro...
  • Quicksort

  • Referenced in 128 articles [sw20694]
  • presortedness measure Inv. Differences close to a factor of two are observed between instances with...
  • CHOLMOD

  • Referenced in 73 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...