DC FieldValueLanguage
dc.contributor.authorRump, Siegfried M.-
dc.contributor.authorBünger, Florian-
dc.contributor.authorJeannerod, Claude Pierre-
dc.date.accessioned2020-03-26T09:03:22Z-
dc.date.available2020-03-26T09:03:22Z-
dc.date.issued2015-03-24-
dc.identifier.citationBIT Numerical Mathematics 1 (56): 293-307 (2016-03-01)de_DE
dc.identifier.issn1572-9125de_DE
dc.identifier.urihttp://hdl.handle.net/11420/5500-
dc.description.abstractLet (Formula presented.) denote the relative rounding error of some floating-point format. Recently it has been shown that for a number of standard Wilkinson-type bounds the typical factors (Formula presented.) can be improved into (Formula presented.) , and that the bounds are valid without restriction on (Formula presented.). Problems include summation, dot products and thus matrix multiplication, residual bounds for (Formula presented.) - and Cholesky-decomposition, and triangular system solving by substitution. In this note we show a similar result for the product (Formula presented.) of real and/or floating-point numbers (Formula presented.) , for computation in any order, and for any base (Formula presented.). The derived error bounds are valid under a mandatory restriction of (Formula presented.). Moreover, we prove a similar bound for Horner’s polynomial evaluation scheme.en
dc.language.isoende_DE
dc.publisherSpringer Science + Business Media B.Vde_DE
dc.relation.ispartofBITde_DE
dc.subjectFloating-point productde_DE
dc.subjectHorner schemede_DE
dc.subjectIEEE 754 standardde_DE
dc.subjectWilkinson type error estimatesde_DE
dc.subject.ddc004: Informatikde_DE
dc.titleImproved error bounds for floating-point products and Horner’s schemede_DE
dc.typeArticlede_DE
dc.type.diniarticle-
dcterms.DCMITypeText-
tuhh.abstract.englishLet (Formula presented.) denote the relative rounding error of some floating-point format. Recently it has been shown that for a number of standard Wilkinson-type bounds the typical factors (Formula presented.) can be improved into (Formula presented.) , and that the bounds are valid without restriction on (Formula presented.). Problems include summation, dot products and thus matrix multiplication, residual bounds for (Formula presented.) - and Cholesky-decomposition, and triangular system solving by substitution. In this note we show a similar result for the product (Formula presented.) of real and/or floating-point numbers (Formula presented.) , for computation in any order, and for any base (Formula presented.). The derived error bounds are valid under a mandatory restriction of (Formula presented.). Moreover, we prove a similar bound for Horner’s polynomial evaluation scheme.de_DE
tuhh.publisher.doi10.1007/s10543-015-0555-z-
tuhh.publication.instituteZuverlässiges Rechnen E-19de_DE
tuhh.type.opus(wissenschaftlicher) Artikel-
dc.type.driverarticle-
dc.type.casraiJournal Article-
tuhh.container.issue1de_DE
tuhh.container.volume56de_DE
tuhh.container.startpage293de_DE
tuhh.container.endpage307de_DE
local.status.inpressfalsede_DE
item.cerifentitytypePublications-
item.openairecristypehttp://purl.org/coar/resource_type/c_6501-
item.fulltextNo Fulltext-
item.creatorOrcidRump, Siegfried M.-
item.creatorOrcidBünger, Florian-
item.creatorOrcidJeannerod, Claude Pierre-
item.openairetypeArticle-
item.languageiso639-1en-
item.creatorGNDRump, Siegfried M.-
item.creatorGNDBünger, Florian-
item.creatorGNDJeannerod, Claude Pierre-
item.grantfulltextnone-
crisitem.author.deptZuverlässiges Rechnen E-19-
crisitem.author.deptZuverlässiges Rechnen E-19-
crisitem.author.deptZuverlässiges Rechnen E-19-
crisitem.author.orcid0000-0002-4779-4800-
crisitem.author.parentorgStudiendekanat Elektrotechnik, Informatik und Mathematik-
crisitem.author.parentorgStudiendekanat Elektrotechnik, Informatik und Mathematik-
crisitem.author.parentorgStudiendekanat Elektrotechnik, Informatik und Mathematik-
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