• LAPACK

  • Referenced in 1211 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 1011 articles [sw04827]
  • functions for constructing test matrices, computing matrix factorizations, visualizing matrices, and carrying out direct search...
  • SINGULAR

  • Referenced in 934 articles [sw00866]
  • Tangent Cone algorithm. Furthermore, it provides polynomial factorizations, resultant, characteristic set and gcd computations, syzygy...
  • REDUCE

  • Referenced in 637 articles [sw00789]
  • extending program syntax; analytic differentiation and integration; factorization of polynomials; facilities for the solution...
  • ARPACK

  • Referenced in 592 articles [sw04218]
  • problems. For many standard problems, a matrix factorization is not required. Only the action...
  • CoCoA

  • Referenced in 482 articles [sw00143]
  • dimensional schemes, Poincare’ series and Hilbert functions, factorization of polynomials, toric ideals. The capabilities...
  • ScaLAPACK

  • Referenced in 328 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...
  • MINOS

  • Referenced in 410 articles [sw05095]
  • basis package (for maintaining sparse LU factors of the basis matrix), automatic scaling of linear...
  • UMFPACK

  • Referenced in 185 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...
  • CGS

  • Referenced in 270 articles [sw08225]
  • preconditioning called ILLU (an incomplete line-LU-factorization). The conclusion of the author is that...
  • symrcm

  • Referenced in 229 articles [sw08566]
  • good preordering for LU or Cholesky factorization of matrices that come from long, skinny problems...
  • ILUT

  • Referenced in 86 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...
  • WEKA

  • Referenced in 144 articles [sw06435]
  • This article provides an overview of the factors that we believe to be important...
  • SuperLU

  • Referenced in 90 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 117 articles [sw02791]
  • critical components in a GRG code: basis factorizations, search directions, line-searches, and Newton iterations...
  • SDPLR

  • Referenced in 83 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...
  • 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...
  • SuperLU-DIST

  • Referenced in 59 articles [sw00002]
  • 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...
  • DEVEX

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