4.5 Article

Algorithm 887: CHOLMOD, Supernodal Sparse Cholesky Factorization and Update/Downdate

Journal

Publisher

ASSOC COMPUTING MACHINERY
DOI: 10.1145/1391989.1391995

Keywords

Algorithms; Experimentation; Performance; Cholesky factorization; linear equations; sparse matrices

Funding

  1. National Science Foundation [0203270, 0620286, 0619080]
  2. Direct For Computer & Info Scie & Enginr
  3. Division of Computing and Communication Foundations [0203270] Funding Source: National Science Foundation
  4. Directorate For Engineering
  5. Div Of Civil, Mechanical, & Manufact Inn [0620286] Funding Source: National Science Foundation
  6. Division Of Mathematical Sciences
  7. Direct For Mathematical & Physical Scien [0619080] Funding Source: National Science Foundation

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CHOLMOD is a set of routines for factorizing sparse symmetric positive definite matrices of the form A or AA(T), updating/downdating a sparse Cholesky factorization, solving linear systems, updating/downdating the solution to the triangular system Lx = b, and many other sparse matrix functions for both symmetric and unsymmetric matrices. Its supernodal Cholesky factorization relies on LAPACK and the Level-3 BLAS, and obtains a substantial fraction of the peak performance of the BLAS. Both real and complex matrices are supported. CHOLMOD is written in ANSI/ISO C, with both C and MATLAB (TM) interfaces. It appears in MATLAB 7.2 as x=A\b when A is sparse symmetric positive definite, as well as in several other sparse matrix functions.

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