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On computational order of convergence of some multi-precision solvers of nonlinear systems of equations

dc.contributor.authorGrau Sánchez, Miguel
dc.contributor.authorGrau Gotés, Maria Àngela
dc.contributor.authorDíaz Barrero, José Luis
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III
dc.date.accessioned2011-05-05T11:25:05Z
dc.date.available2011-05-05T11:25:05Z
dc.date.issued2011-05-02
dc.identifier.urihttp://hdl.handle.net/2117/12475
dc.descriptionReport d'un treball de recerca on es presenten noves tècniques de càlcul de l'ordre de convergència amb una aritmètica adaptativa.
dc.description.abstractIn this paper the local order of convergence used in iterative methods to solve nonlinear systems of equations is revisited, where shorter alternative analytic proofs of the order based on developments of multilineal functions are shown. Most important, an adaptive multi-precision arithmetics is used hereof, where in each step the length of the mantissa is defined independently of the knowledge of the root. Furthermore, generalizations of the one dimensional case to m-dimensions of three approximations of computational order of convergence are defined. Examples illustrating the previous results are given.
dc.format.extent14 p.
dc.language.isoeng
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 Spain
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica
dc.subject.lcshNonlinear systems
dc.subject.lcshIterative methods (Mathematics)
dc.subject.lcshNumerical analysis
dc.subject.lcshConvergence
dc.titleOn computational order of convergence of some multi-precision solvers of nonlinear systems of equations
dc.typeExternal research report
dc.subject.lemacMètodes iteratius (Matemàtica)
dc.subject.lemacAnàlisi numèrica
dc.subject.lemacConvergència (Matemàtica)
dc.contributor.groupUniversitat Politècnica de Catalunya. NRG - Riscos Naturals i Geoestadística
dc.contributor.groupUniversitat Politècnica de Catalunya. MMAC - Models Matemàtics aplicats a les ciencies humanes i de la natura
dc.subject.amsClassificació AMS::65 Numerical analysis::65H Nonlinear algebraic or transcendental equations
dc.subject.amsClassificació AMS::41 Approximations and expansions
dc.rights.accessOpen Access
drac.iddocument5714632
dc.description.versionPreprint


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