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...

Ausführliche Beschreibung

Bibliographische Detailangaben

Veröffentlicht in:	SIAM journal on matrix analysis and applications Jg. 34; H. 2; S. 338 - 344
Hauptverfasser:	Jeannerod, Claude-Pierre, Rump, Siegfried M.
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Philadelphia Society for Industrial and Applied Mathematics 01.01.2013
Schlagworte:	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-Zugang:	Volltext
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!