A fully portable high performance minimal storage hybrid format Cholesky algorithm

Autor:	John Reid, Jerzy Waśniewski, Bjarne Stig Andersen, Fred G. Gustavson, John A. Gunnels
Rok vydání:	2005
Předmět:	Matrix (mathematics) Applied Mathematics Matrix representation Linear system Linear algebra Code (cryptography) Minimum degree algorithm Positive-definite matrix Algorithm Software Cholesky decomposition Mathematics
Zdroj:	ACM Transactions on Mathematical Software. 31:201-227
ISSN:	1557-7295 0098-3500
DOI:	10.1145/1067967.1067969
Popis:	We consider the efficient implementation of the Cholesky solution of symmetric positive-definite dense linear systems of equations using packed storage. We take the same starting point as that of LINPACK and LAPACK, with the upper (or lower) triangular part of the matrix stored by columns. Following LINPACK and LAPACK, we overwrite the given matrix by its Cholesky factor. We consider the use of a hybrid format in which blocks of the matrices are held contiguously and compare this to the present LAPACK code. Code based on this format has the storage advantages of the present code but substantially outperforms it. Furthermore, it compares favorably to using conventional full format (LAPACK) and using the recursive format of Andersen et al. [2001].
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::0e05a1d879b18e8be4a7cade878ffb6f https://doi.org/10.1145/1067967.1067969 Zobrazit plný text záznamu