## 2006.169: Stability of a method for multiplying complex matrices with three real matrix multiplications

2006.169:
Nicholas J. Higham
(1992)
*Stability of a method for multiplying complex matrices with three real matrix multiplications.*
SIAM Journal On Matrix Analysis And Applications, 13 (3).
pp. 681-687.
ISSN 1095-7162

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Official URL: http://locus.siam.org/SIMAX/volume-13/art_0613043.html

## Abstract

By use of a simple identity, the product of two complex matrices can be formed with three real matrix multiplications and five real matrix additions, instead of the four real matrix multiplications and two real matrix additions required by the conventional approach. This alternative method reduces the number of arithmetic operations, even for small dimensions, achieving a saving of up to 25 percent. The numerical stability of the method is investigated. The method is found to be less stable than conventional multiplication but stable enough to warrant practical use. Issues involved in the choice of method for complex matrix multiplication are discussed, including the relative efficiency of real and complex arithmetic and the backward stability of block algorithms.

Item Type: | Article |
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Uncontrolled Keywords: | matrix multiplication, complex matrix, Strassen’s method, Winograd’s identity, numerical stability, error analysis, level-3 BLAS |

Subjects: | MSC 2000 > 15 Linear and multilinear algebra; matrix theory MSC 2000 > 65 Numerical analysis |

MIMS number: | 2006.169 |

Deposited By: | Miss Louise Stait |

Deposited On: | 03 July 2006 |

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