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- Title
Error-free transformation of matrix multiplication with a posteriori validation.
- Authors
Ozaki, Katsuhisa; Ogita, Takeshi; Oishi, Shin'ichi
- Abstract
In this study, we examine the accurate matrix multiplication in floating-point arithmetic. We demonstrate the error-free transformations of matrix multiplication using high performance basic linear algebra subprograms. These transformations can be applied to accurately compute the product of two matrices using floating-point entries. A key technique for this calculation is error-free splitting in floating-point matrices. In this study, we improve upon our previous method by a posteriori validation using floating-point exception. In the method, we utilize the presence of overflow in a positive manner for detecting whether rounding error occurs. If overflow occurs, the result contains some exceptional values such as
- Subjects
ERROR analysis in mathematics; MATHEMATICAL transformations; MATRICES (Mathematics); MULTIPLICATION; LINEAR algebra; FLOATING-point arithmetic
- Publication
Numerical Linear Algebra with Applications, 2016, Vol 23, Issue 5, p931
- ISSN
1070-5325
- Publication type
Article
- DOI
10.1002/nla.2061