### Abstract

This paper is concerned with the tight enclosure of matrix multiplication AB for two floating-point matrices A and B. The aim of this paper is to compute component-wise upper and lower bounds of the exact result C of the matrix multiplication AB by floating-point arithmetic. Namely, an interval matrix enclosing C is obtained. In this paper, new algorithms for enclosing C are proposed. The proposed algorithms are designed to mainly exploit the level 3 operations in BLAS. Although the proposed algorithms take around twice as much costs as a standard algorithm promoted by Oishi and Rump, the accuracy of the result by the proposed algorithms is better than that of the standard algorithm. At the end of this paper, we present numerical examples showing the efficiency of the proposed algorithms.

Original language | English |
---|---|

Pages (from-to) | 237-248 |

Number of pages | 12 |

Journal | Numerical Linear Algebra with Applications |

Volume | 18 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2011 Mar |

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### Keywords

- Interval arithmetic
- Matrix multiplication
- Verified numerical computation

### ASJC Scopus subject areas

- Algebra and Number Theory
- Applied Mathematics

### Cite this

*Numerical Linear Algebra with Applications*,

*18*(2), 237-248. https://doi.org/10.1002/nla.724

**Tight and efficient enclosure of matrix multiplication by using optimized BLAS.** / Ozaki, Katsuhisa; Ogita, Takeshi; Oishi, Shin'ichi.

Research output: Contribution to journal › Article

*Numerical Linear Algebra with Applications*, vol. 18, no. 2, pp. 237-248. https://doi.org/10.1002/nla.724

}

TY - JOUR

T1 - Tight and efficient enclosure of matrix multiplication by using optimized BLAS

AU - Ozaki, Katsuhisa

AU - Ogita, Takeshi

AU - Oishi, Shin'ichi

PY - 2011/3

Y1 - 2011/3

N2 - This paper is concerned with the tight enclosure of matrix multiplication AB for two floating-point matrices A and B. The aim of this paper is to compute component-wise upper and lower bounds of the exact result C of the matrix multiplication AB by floating-point arithmetic. Namely, an interval matrix enclosing C is obtained. In this paper, new algorithms for enclosing C are proposed. The proposed algorithms are designed to mainly exploit the level 3 operations in BLAS. Although the proposed algorithms take around twice as much costs as a standard algorithm promoted by Oishi and Rump, the accuracy of the result by the proposed algorithms is better than that of the standard algorithm. At the end of this paper, we present numerical examples showing the efficiency of the proposed algorithms.

AB - This paper is concerned with the tight enclosure of matrix multiplication AB for two floating-point matrices A and B. The aim of this paper is to compute component-wise upper and lower bounds of the exact result C of the matrix multiplication AB by floating-point arithmetic. Namely, an interval matrix enclosing C is obtained. In this paper, new algorithms for enclosing C are proposed. The proposed algorithms are designed to mainly exploit the level 3 operations in BLAS. Although the proposed algorithms take around twice as much costs as a standard algorithm promoted by Oishi and Rump, the accuracy of the result by the proposed algorithms is better than that of the standard algorithm. At the end of this paper, we present numerical examples showing the efficiency of the proposed algorithms.

KW - Interval arithmetic

KW - Matrix multiplication

KW - Verified numerical computation

UR - http://www.scopus.com/inward/record.url?scp=79951820141&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79951820141&partnerID=8YFLogxK

U2 - 10.1002/nla.724

DO - 10.1002/nla.724

M3 - Article

AN - SCOPUS:79951820141

VL - 18

SP - 237

EP - 248

JO - Numerical Linear Algebra with Applications

JF - Numerical Linear Algebra with Applications

SN - 1070-5325

IS - 2

ER -