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

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 roundi...

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Bibliographic Details
Published in:Journal of physics. Conference series 2020-03, Vol.1490 (1), p.12062
Main Author: Ozaki, Katsuhisa
Format: Article
Language:English
Subjects:
Algorithms
Error analysis
Floating point arithmetic
Linear algebra
Mathematical analysis
Mathematicians
Matrices (mathematics)
Multiplication
Multiplication & division
Physics
Rounding
Transformations (mathematics)
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Summary: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.
ISSN:1742-6588
1742-6596
DOI:10.1088/1742-6596/1490/1/012062