TY - JOUR

T1 - An Error-Free Transformation for Matrix Multiplication with Reproducible Algorithms and Divide and Conquer Methods

AU - Ozaki, Katsuhisa

N1 - Publisher Copyright:
© Published under licence by IOP Publishing Ltd.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/6/9

Y1 - 2020/6/9

N2 - 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.

AB - 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.

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U2 - 10.1088/1742-6596/1490/1/012062

DO - 10.1088/1742-6596/1490/1/012062

M3 - Conference article

AN - SCOPUS:85088096073

VL - 1490

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

SN - 1742-6588

IS - 1

M1 - 012062

T2 - 5th International Conference on Mathematics: Pure, Applied and Computation, ICoMPAC 2019

Y2 - 19 October 2019

ER -