• UMFPACK

  • Referenced in 421 articles [sw00989]
  • ordering and symbolic analysis phase computes an upper bound on fill-in, work, and memory ... provided for ordering and analyzing a sparse matrix, computing the numerical factorization, solving a system ... factors, transposing and permuting a sparse matrix, and converting between sparse matrix representations.\parThe simple...
  • SPARSKIT

  • Referenced in 228 articles [sw07692]
  • SPARSKIT: A basic toolkit for sparse matrix computations. This paper presents the main features ... tool package for manipulating and working with sparse matrices. One of the goals ... software and data between researchers in sparse matrix computations. Our starting point is the Harwell/Boeing ... matrix, plotting a matrix pro le, performing basic linear algebra operations with sparse matrices...
  • CSparse

  • Referenced in 238 articles [sw20382]
  • linear systems. Computational scientists often encounter problems requiring the solution of sparse systems of linear ... algorithms, and data structures found in sparse matrix software libraries. Here, Davis presents the fundamentals ... also explains how MATLAB performs its sparse matrix computations...
  • LAPACK

  • Referenced in 1713 articles [sw00503]
  • problems, and singular value problems. The associated matrix factorizations (LU, Cholesky, QR, SVD, Schur, generalized ... Schur) are also provided, as are related computations such as reordering of the Schur factorizations ... banded matrices are handled, but not general sparse matrices. In all areas, similar functionality ... algorithms to use block matrix operations, such as matrix multiplication, in the innermost loops. These...
  • ARPACK

  • Referenced in 848 articles [sw04218]
  • compute a few eigenvalues and corresponding eigenvectors of a general n by n matrix ... 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, a matrix factorization is not required. Only the action of the matrix...
  • JDQZ

  • Referenced in 610 articles [sw07031]
  • JDQZ algorithm can be used for computing a few selected eigenvalues with some desirable property ... together with the associated eigenvectors of a matrix pencil A-lambda*B. The matrices ... sparse and of large size. The Jacobi-Davidson method is used to compute a partial...
  • PLCP

  • Referenced in 238 articles [sw04795]
  • matrix A may be either full or sparse; computations are made accordingly. This...
  • JDQR

  • Referenced in 513 articles [sw04021]
  • JDQR algorithm can be used for computing a few selected eigenvalues with some desirable property ... associated eigenvectors of a matrix A. The matrix can be real or complex, Hermitian ... sparse and of large size. The Jacobi-Davidson method is used to compute a partial...
  • Expokit

  • Referenced in 200 articles [sw00258]
  • computes either a small matrix exponential in full, the action of a large sparse matrix ... backbone of the sparse routines consists of matrix-free Krylov subspace projection methods (Arnoldi ... toolkit is capable of coping with sparse matrices of large dimension. The software handles real ... symmetric and Hermitian matrices. The computation of matrix exponentials is a numerical issue of critical...
  • symrcm

  • Referenced in 390 articles [sw08566]
  • nonsymmetric S. For a real, symmetric sparse matrix, S, the eigenvalues ... probably takes less time to compute than...
  • SparseMatrix

  • Referenced in 747 articles [sw04629]
  • development and performance evaluation of sparse matrix algorithms. It allows for robust and repeatable experiments ... geometry (as structural engineering, computational fluid dynamics, model reduction, electromagnetics, semiconductor devices, thermodynamics, materials, acoustics...
  • P-SPARSLIB

  • Referenced in 35 articles [sw01455]
  • develop a portable FORTRAN routine for sparse matrix computation. It emphasizes iterative techniques...
  • Meschach

  • Referenced in 85 articles [sw01112]
  • language library of routines for performing matrix computations. It has a collection of data structures ... integer vectors, complex vectors and matrices and sparse matrices...
  • softImpute

  • Referenced in 83 articles [sw12263]
  • special sparse-matrix class named ”Incomplete” that efficiently handles all computations. The package includes procedures ... both, and for computing low-rank SVDs on large sparse centered matrices (i.e. principal components...
  • INTLAB

  • Referenced in 472 articles [sw04004]
  • complex sparse matrices (very fast) automatic differentiation (forward mode, vectorized computations, fast) Gradients (to solve ... inner inclusions) accurate summation, dot product and matrix-vector residuals (interpreted, reference implementation, slow) multiple...
  • TRIC

  • Referenced in 47 articles [sw02165]
  • essentially requires the computation of a sparse 9 by 9 matrix. The element formulation departs...
  • SelInv

  • Referenced in 31 articles [sw13937]
  • algorithm for computing selected elements of a general sparse symmetric matrix A that ... LDLT factorization of A. We discuss how computational efficiency can be gained by making ... performance of SelInv on a collection of sparse matrices of various sizes and nonzero structures...
  • TensorToolbox

  • Referenced in 185 articles [sw04185]
  • tensors using coordinate format and describe the computational efficiency of this scheme for various mathematical ... itself may be dense, sparse, or factored) and a matrix along each mode ... demonstrate that many elementary operations can be computed using only the components...
  • UTV

  • Referenced in 272 articles [sw05213]
  • original package. We provide algorithms for computing and modifying symmetric rank-revealing VSV decompositions ... matrix pair to handle interference-type problems with a rank-deficient covariance matrix ... dominant singular values of a sparse or structured matrix. These new algorithms have applications...