Matrix multiplication with guaranteed accuracy by level 3 BLAS

Katsuhisa Ozaki; Takeshi Ogita; Shin'ichi Oishi

doi:10.1063/1.4772125

Matrix multiplication with guaranteed accuracy by level 3 BLAS

Katsuhisa Ozaki, Takeshi Ogita, Shin'ichi Oishi

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

This paper is concerned with an accurate computing for matrix multiplication. We show that matrix multiplication can be transformed into a summation of floating-point matrices by mainly using level 3 operations in BLAS. We call it 'errorfree transformation of matrix multiplication'. By combining this error-free transformation and accurate summation algorithms for floating-point numbers, we can obtain an accurate result of matrix multiplication. Numerical examples are presented to illustrate the efficiency of the proposed algorithm.

Original language	English
Title of host publication	International Conference of Computational Methods in Sciences and Engineering 2009, ICCMSE 2009
Pages	1128-1133
Number of pages	6
DOIs	https://doi.org/10.1063/1.4772125
Publication status	Published - 2012
Externally published	Yes
Event	International Conference of Computational Methods in Sciences and Engineering 2009, ICCMSE 2009 - Rhodes, Greece Duration: 2009 Sept 29 → 2009 Oct 4

Publication series

Name	AIP Conference Proceedings
Volume	1504
ISSN (Print)	0094-243X
ISSN (Electronic)	1551-7616

Conference

Conference	International Conference of Computational Methods in Sciences and Engineering 2009, ICCMSE 2009
Country/Territory	Greece
City	Rhodes
Period	09/9/29 → 09/10/4

Keywords

Accurate Algorithms
Matrix Computations

ASJC Scopus subject areas

Physics and Astronomy(all)

Access to Document

10.1063/1.4772125

Cite this

Ozaki, K, Ogita, T & Oishi, S 2012, Matrix multiplication with guaranteed accuracy by level 3 BLAS. in International Conference of Computational Methods in Sciences and Engineering 2009, ICCMSE 2009. AIP Conference Proceedings, vol. 1504, pp. 1128-1133, International Conference of Computational Methods in Sciences and Engineering 2009, ICCMSE 2009, Rhodes, Greece, 09/9/29. https://doi.org/10.1063/1.4772125

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AB - This paper is concerned with an accurate computing for matrix multiplication. We show that matrix multiplication can be transformed into a summation of floating-point matrices by mainly using level 3 operations in BLAS. We call it 'errorfree transformation of matrix multiplication'. By combining this error-free transformation and accurate summation algorithms for floating-point numbers, we can obtain an accurate result of matrix multiplication. Numerical examples are presented to illustrate the efficiency of the proposed algorithm.

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ER -

Matrix multiplication with guaranteed accuracy by level 3 BLAS

Abstract

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Conference

Keywords

ASJC Scopus subject areas

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