Matrix multiplication with guaranteed accuracy by level 3 BLAS

Katsuhisa Ozaki, Takeshi Ogita, Shin'ichi Oishi

Research output: Chapter in Book/Report/Conference proceedingConference 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 languageEnglish
Title of host publicationAIP Conference Proceedings
Pages1128-1133
Number of pages6
Volume1504
DOIs
Publication statusPublished - 2012
Externally publishedYes
EventInternational Conference of Computational Methods in Sciences and Engineering 2009, ICCMSE 2009 - Rhodes
Duration: 2009 Sep 292009 Oct 4

Other

OtherInternational Conference of Computational Methods in Sciences and Engineering 2009, ICCMSE 2009
CityRhodes
Period09/9/2909/10/4

Fingerprint

multiplication
matrices
floating

Keywords

  • Accurate Algorithms
  • Matrix Computations

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Ozaki, K., Ogita, T., & Oishi, S. (2012). Matrix multiplication with guaranteed accuracy by level 3 BLAS. In AIP Conference Proceedings (Vol. 1504, pp. 1128-1133) https://doi.org/10.1063/1.4772125

Matrix multiplication with guaranteed accuracy by level 3 BLAS. / Ozaki, Katsuhisa; Ogita, Takeshi; Oishi, Shin'ichi.

AIP Conference Proceedings. Vol. 1504 2012. p. 1128-1133.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Ozaki, K, Ogita, T & Oishi, S 2012, Matrix multiplication with guaranteed accuracy by level 3 BLAS. in AIP Conference Proceedings. vol. 1504, pp. 1128-1133, International Conference of Computational Methods in Sciences and Engineering 2009, ICCMSE 2009, Rhodes, 09/9/29. https://doi.org/10.1063/1.4772125
Ozaki K, Ogita T, Oishi S. Matrix multiplication with guaranteed accuracy by level 3 BLAS. In AIP Conference Proceedings. Vol. 1504. 2012. p. 1128-1133 https://doi.org/10.1063/1.4772125
Ozaki, Katsuhisa ; Ogita, Takeshi ; Oishi, Shin'ichi. / Matrix multiplication with guaranteed accuracy by level 3 BLAS. AIP Conference Proceedings. Vol. 1504 2012. pp. 1128-1133
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