### Abstract

This paper discusses accurate numerical algorithms for matrix multiplication. Matrix multiplication is a basic and important problem in numerical linear algebra. Numerical computations using floating-point arithmetic can be quickly performed on existing computers. However, the accumulation of rounding errors due to finite precision arithmetic is a critical problem. An error-free transformation for matrix multiplication is reviewed in this paper. Such a transformation is extremely useful for developing accurate numerical algorithms for matrix multiplication. One advantage of the transformation is that it exploits Basic Linear Algebra Subprograms (BLAS). We provide a rounding error analysis of reproducible algorithms for matrix multiplication based on the error-free transformation. In addition, we propose an error-free transformation for matrix multiplication that can be utilized with the divide and conquer methods.

Original language | English |
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Article number | 012062 |

Journal | Journal of Physics: Conference Series |

Volume | 1490 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2020 Jun 9 |

Event | 5th International Conference on Mathematics: Pure, Applied and Computation, ICoMPAC 2019 - Surabaya, Indonesia Duration: 2019 Oct 19 → … |

### ASJC Scopus subject areas

- Physics and Astronomy(all)