Improved Error Bounds for Inner Products in Floating-Point Arithmetic

Given two floating-point vectors $x,y$ of dimension $n$ and assuming rounding to nearest, we show that if no underflow or overflow occurs, any evaluation order for an inner product returns a floating-point number ${\widehat r}$ such that $|{\widehat r}- x^Ty| \leqslant nu|x|^T|y|$ with $u$ the unit...

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Bibliographic Details

Published in:	SIAM journal on matrix analysis and applications Vol. 34; no. 2; pp. 338 - 344
Main Authors:	Jeannerod, Claude-Pierre, Rump, Siegfried M.
Format:	Journal Article
Language:	English
Published:	Philadelphia Society for Industrial and Applied Mathematics 01.01.2013
Subjects:	Approximation Arithmetic Computer Arithmetic Computer Science Constrictions Errors Floating point arithmetic Mathematical analysis Numerical Analysis Product returns Rounding Vectors (mathematics) rounding error analysis unit in the first place floating-point inner product
ISSN:	0895-4798, 1095-7162
Online Access:	Get full text
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