### 抜粋

In this study, we examine the accurate matrix multiplication in floating-point arithmetic. We demonstrate the error-free transformations of matrix multiplication using high performance basic linear algebra subprograms. These transformations can be applied to accurately compute the product of two matrices using floating-point entries. A key technique for this calculation is error-free splitting in floating-point matrices. In this study, we improve upon our previous method by a posteriori validation using floating-point exception. In the method, we utilize the presence of overflow in a positive manner for detecting whether rounding error occurs. If overflow occurs, the result contains some exceptional values such as ±∞ and NaN, that is, the method fails by necessity. Otherwise, we can confirm that no rounding error occurs in the process. Therefore, reducing the possibility of overflow is important. The numerical results suggest that the proposed algorithm provides more accurate results compared with the original algorithm. Moreover, for the product of n × n matrices, when n ≥5000, the new algorithm reduces the computing time for error-free transformation by an average of 20 % and up to 30 % compared with the original algorithm. Furthermore, the new algorithm can be used when matrix multiplication is performed using divide-and-conquer methods.

元の言語 | English |
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ページ（範囲） | 931-946 |

ページ数 | 16 |

ジャーナル | Numerical Linear Algebra with Applications |

巻 | 23 |

発行部数 | 5 |

DOI | |

出版物ステータス | Published - 2016 10 1 |

### ASJC Scopus subject areas

- Algebra and Number Theory
- Applied Mathematics

## フィンガープリント Error-free transformation of matrix multiplication with a posteriori validation' の研究トピックを掘り下げます。これらはともに一意のフィンガープリントを構成します。

## これを引用

*Numerical Linear Algebra with Applications*,

*23*(5), 931-946. https://doi.org/10.1002/nla.2061