Dynamic supernodes in sparse Cholesky update/downdate and triangular solves
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| Title: | Dynamic supernodes in sparse Cholesky update/downdate and triangular solves |
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| Authors: | Timothy A. Davis, William W. Hager |
| Contributors: | The Pennsylvania State University CiteSeerX Archives |
| Source: | http://www.cise.ufl.edu/~davis/techreports/cholmod/tr06-004.pdf. |
| Publication Year: | 2006 |
| Collection: | CiteSeerX |
| Description: | The supernodal method for sparse Cholesky factorization represents the factor L as a set of supernodes, each consisting of a contiguous set of columns of L with identical nonzero pattern. A conventional supernode is stored as a dense submatrix. While this is suitable for sparse Cholesky factorization where the nonzero pattern of L does not change, it is not suitable for methods that modify a sparse Cholesky factorization after a low-rank change to A (an update/downdate, A = A±WW T). Supernodes merge and split apart during an update/downdate. Dynamic supernodes are introduced, which allow a sparse Cholesky update/downdate to obtain performance competitive with conventional supernodal methods. A dynamic supernodal solver is shown to exceed the performance of the conventional (BLAS-based) supernodal method for solving triangular systems. These methods are incorporated into CHOLMOD, a sparse Cholesky factorization and update/downdate package, which forms the basis of x=A\b in MAT-LAB when A is sparse and symmetric positive definite. 1 |
| Document Type: | text |
| File Description: | application/pdf |
| Language: | English |
| Relation: | http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.135.2462 |
| Availability: | http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.135.2462 http://www.cise.ufl.edu/~davis/techreports/cholmod/tr06-004.pdf |
| Rights: | Metadata may be used without restrictions as long as the oai identifier remains attached to it. |
| Accession Number: | edsbas.179FC5AB |
| Database: | BASE |
Nájsť tento článok vo Web of Science | Abstract: | The supernodal method for sparse Cholesky factorization represents the factor L as a set of supernodes, each consisting of a contiguous set of columns of L with identical nonzero pattern. A conventional supernode is stored as a dense submatrix. While this is suitable for sparse Cholesky factorization where the nonzero pattern of L does not change, it is not suitable for methods that modify a sparse Cholesky factorization after a low-rank change to A (an update/downdate, A = A±WW T). Supernodes merge and split apart during an update/downdate. Dynamic supernodes are introduced, which allow a sparse Cholesky update/downdate to obtain performance competitive with conventional supernodal methods. A dynamic supernodal solver is shown to exceed the performance of the conventional (BLAS-based) supernodal method for solving triangular systems. These methods are incorporated into CHOLMOD, a sparse Cholesky factorization and update/downdate package, which forms the basis of x=A\b in MAT-LAB when A is sparse and symmetric positive definite. 1 |
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