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Block Algorithm and Its Implementation for Cholesky Factorization

Authors:
Jianping Chen
Zhe Jin
Quan Shi
Jianlin Qiu
Weifu Liu

Keywords: Numerical computation; Cholesky factorization; matrix blocking; cache use.

Abstract:
Block algorithm divides a large matrix into small blocks of submatrices to make full use of computer’s caches. Blocked smaller submatrices can be directly loaded into the caches to compute. The efficiency of the computation is hence improved. The block algorithm for Cholesky factorization is studied in this paper. Detai1ed derivation and implementation of the block algorithm are presented. The computations of modules involved in the block algorithm are discussed. A C++ language program is developed. It is tested and compared with the standard (unblocked) version of the Cholesky factorization. The testing results show that the presented block algorithm outperforms the unblocked one in the cases of large matrices, with an increase of execution speed of 20%.

Pages: 232 to 236

Copyright: Copyright (c) IARIA, 2013

Publication date: July 21, 2013

Published in: conference

ISSN: 2308-4529

ISBN: 978-1-61208-283-7

Location: Nice, France

Dates: from July 21, 2013 to July 26, 2013