• # ARPACK

• Referenced in 841 articles [sw04218]
• Arnoldi Method (IRAM). When the matrix A is symmetric it reduces to a variant ... scale problems. For many standard problems, a matrix factorization is not required. Only the action ... matrix on a vector is needed. ARPACK software is capable of solving large scale symmetric...
• # CHOLMOD

• Referenced in 113 articles [sw04412]
• routines for factorizing sparse symmetric positive definite matrices of the form A or AAT, updating/downdating ... many other sparse matrix functions for both symmetric and unsymmetric matrices. Its supernodal Cholesky factorization ... sparse symmetric positive definite, as well as in several other sparse matrix functions...
• # Expokit

• Referenced in 198 articles [sw00258]
• backbone of the sparse routines consists of matrix-free Krylov subspace projection methods (Arnoldi ... specific routines for symmetric and Hermitian matrices. The computation of matrix exponentials is a numerical...
• # DSPCA

• Referenced in 35 articles [sw04804]
• Frobenius-norm sense, a positive, semidefinite symmetric matrix by a rank-one matrix, with ... arises in the decomposition of a covariance matrix into sparse factors, and has wide applications ... largest eigenvalue of a symmetric matrix, where cardinality is constrained, and derive a semidefinite programming...
• # MUMPS

• Referenced in 502 articles [sw04013]
• systems with symmetric positive definite matrices; general symmetric matrices; general unsymmetric matrices; Version for complex ... Iterative refinement and backward error analysis; Various matrix input formats assembled format; distributed assembled format...
• # BEAN

• Referenced in 72 articles [sw09636]
• attractive feature of producing a symmetric coefficient matrix. In addition, the Galerkin approximation allows standard...
• # ScaLAPACK

• Referenced in 417 articles [sw00830]
• iterative refinement, for LU and Cholesky factorization, matrix inversion, full-rank linear least squares problems ... bidiagonal and tridiagonal form, reduction of a symmetric-definite/Hermitian-definite generalized eigenproblem to standard form ... solvers for LU, Cholesky, and QR, the matrix sign function for eigenproblems...
• # SelInv

• Referenced in 30 articles [sw13937]
• Selected Inversion of a Sparse Symmetric Matrix. We describe an efficient implementation of an algorithm ... selected elements of a general sparse symmetric matrix A that can be decomposed...
• # UTV

• Referenced in 263 articles [sw05213]
• provide algorithms for computing and modifying symmetric rank-revealing VSV decompositions, we expand the algorithms ... ULLV decomposition of a matrix pair to handle interference-type problems with a rank-deficient...
• # DVDSON

• Referenced in 16 articles [sw17845]
• eigenpairs of a large, sparse, real, symmetric matrix A program is presented for determining ... spectrum of a large, real, symmetric matrix. Based on the Davidson method, which is extensively...
• # TAUCS

• Referenced in 32 articles [sw04014]
• supernodal solvers when it factors a matrix completely, but it can drop small elements from ... structured matrices. All of these are symmetric orderings. Matrix Operations. Matrix-vector multiplication, triangular solvers...
• # SOLAR

• Referenced in 17 articles [sw08711]
• memory and distributed-memory machines, and its matrix input-output library supports both conventional ... core positive-definite symmetric matrix at a rate exceeding 215 Mflops...
• # Algorithm 840

• Referenced in 26 articles [sw04463]
• prolate differential equation; this yields a symmetric tridiagonal matrix. The prolate functions are then defined ... whose coefficients are the eigenfunctions of the matrix eigenproblem. The grid points and weights ... with $c$ are well-approximated by a symmetric parabola over the whole range of interest...