Reducing Floating Point Error in Dot Product Using the Superblock Family of Algorithms

Autor:	Anthony M. Castaldo, R. Clint Whaley, Anthony T. Chronopoulos
Rok vydání:	2009
Předmět:	Computational Mathematics Floating point Error analysis Applied Mathematics Numerical analysis Linear algebra Dot product Pairwise comparison Upper and lower bounds Algorithm Mathematics Block (data storage)
Zdroj:	SIAM Journal on Scientific Computing. 31:1156-1174
ISSN:	1095-7197 1064-8275
DOI:	10.1137/070679946
Popis:	This paper discusses both the theoretical and statistical errors obtained by various well-known dot products, from the canonical to pairwise algorithms, and introduces a new and more general framework that we have named superblock which subsumes them and permits a practitioner to make trade-offs between computational performance, memory usage, and error behavior. We show that algorithms with lower error bounds tend to behave noticeably better in practice. Unlike many such error-reducing algorithms, superblock requires no additional floating point operations and should be implementable with little to no performance loss, making it suitable for use as a performance-critical building block of a linear algebra kernel.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::114e0a98032723e591ac8f6a47540755 https://doi.org/10.1137/070679946 Zobrazit plný text záznamu Plný text ve formátu PDF