JP Journal of Algebra, Number Theory and Applications
Volume 31, Issue 1, Pages 51 - 74
(November 2013)
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ALGEBRAS OVER FLOATING POINT NUMBERS
Fumiya Suenobu, Masaaki Ito and Fujio Kubo
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Abstract: We find a closest associative multiplication to any multiplication within the decimal floating point arithmetic of finite precision and compare their effect on a computation. The discussion in this article makes an interesting and challenging strategy of a multiplication replacement in computation more practical. To analyze errors, we introduce a notion of an algebra over floating point numbers. |
Keywords and phrases: associative algebras, closest structures, floating point numbers, finite precision. |
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