Please use this identifier to cite or link to this item: https://doi.org/10.15480/882.295
DC FieldValueLanguage
dc.contributor.authorRump, Siegfried M.-
dc.date.accessioned2008-03-19T15:37:27Zde_DE
dc.date.available2008-03-19T15:37:27Zde_DE
dc.date.issued1992de_DE
dc.identifier.citationComputing 47:337-353, 1992de_DE
dc.identifier.urihttp://tubdok.tub.tuhh.de/handle/11420/297-
dc.description.abstractIn the literature efficient algorithms have been described for calculating guaranteed inclusions for the solution of a number of standard numerical problems [3], [4], [8], [11], [12], [13]. The inclusions are given by means of a set containing the solution. In [12], [13] this set is calculated using an affine iteration which is stopped when a nonempty and compact set is mapped into itself. For exactly given input data (point data) it has been shown that this iteration stops if and only if the iteration matrix is convergent (cf. [13]). In this paper we give a necessary and sufficient stopping criterion for the above mentioned iteration for interval input data and interval operations. Stopping is equivalent to the fact that the algorithm presented in [12] for solving interval linear systems computes an inclusion of the solution. An algorithm given by Neumaier is discussed and an algorithm is proposed combining the advantages of our algorithm and a modification of Neumaier's. The combined algorithm yields tight bounds for input intervals of small and large diameter. Using a paper by Jansson [6], [7] we give a quite different geometrical interpretation of inclusion methods. It can be shown that our inclusion methods are optimal in a specified geometrical sense. For another class of sets, for standard simplices, we give some interesting examples.en
dc.language.isoende_DE
dc.rightsinfo:eu-repo/semantics/openAccess-
dc.rights.urihttp://doku.b.tu-harburg.de/doku/lic_ohne_pod.phpde
dc.subjectlinear systemde_DE
dc.subjectiterationde_DE
dc.subjectinclusion methodde_DE
dc.titleOn the Solution of Interval Linear Systemsde_DE
dc.typeArticlede_DE
dc.date.updated2008-03-31T16:10:40Zde_DE
dc.identifier.urnurn:nbn:de:gbv:830-tubdok-3679de_DE
dc.identifier.doi10.15480/882.295-
dc.type.diniarticle-
dc.subject.gndLineares Systemde
dc.subject.gndIterationsverfahrende
dc.subject.gndInklusionde
dc.subject.ddccode510-
dcterms.DCMITypeTextde_DE
tuhh.identifier.urnurn:nbn:de:gbv:830-tubdok-3679de_DE
tuhh.publikation.typarticlede_DE
tuhh.publikation.sourceComputing 47:337-353, 1992de_DE
tuhh.opus.id367de_DE
tuhh.oai.showtruede_DE
tuhh.pod.allowedfalsede_DE
dc.identifier.hdl11420/297-
tuhh.abstract.englishIn the literature efficient algorithms have been described for calculating guaranteed inclusions for the solution of a number of standard numerical problems [3], [4], [8], [11], [12], [13]. The inclusions are given by means of a set containing the solution. In [12], [13] this set is calculated using an affine iteration which is stopped when a nonempty and compact set is mapped into itself. For exactly given input data (point data) it has been shown that this iteration stops if and only if the iteration matrix is convergent (cf. [13]). In this paper we give a necessary and sufficient stopping criterion for the above mentioned iteration for interval input data and interval operations. Stopping is equivalent to the fact that the algorithm presented in [12] for solving interval linear systems computes an inclusion of the solution. An algorithm given by Neumaier is discussed and an algorithm is proposed combining the advantages of our algorithm and a modification of Neumaier's. The combined algorithm yields tight bounds for input intervals of small and large diameter. Using a paper by Jansson [6], [7] we give a quite different geometrical interpretation of inclusion methods. It can be shown that our inclusion methods are optimal in a specified geometrical sense. For another class of sets, for standard simplices, we give some interesting examples.de_DE
tuhh.publication.instituteZuverlässiges Rechnen E-19de_DE
tuhh.identifier.doi10.15480/882.295-
tuhh.type.opus(wissenschaftlicher) Artikelde
tuhh.institute.germanZuverlässiges Rechnen E-19de
tuhh.institute.englishReliable Computing E-19en
tuhh.institute.id38de_DE
tuhh.type.id2de_DE
tuhh.gvk.hasppnfalse-
dc.type.driverarticle-
dc.identifier.oclc930768453-
dc.type.casraiJournal Articleen
item.fulltextWith Fulltext-
item.creatorOrcidRump, Siegfried M.-
item.creatorGNDRump, Siegfried M.-
item.grantfulltextopen-
crisitem.author.deptZuverlässiges Rechnen E-19-
crisitem.author.orcid0000-0002-4779-4800-
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