On computational order of convergence of some multi-precision solvers of nonlinear systems of equations
dc.contributor.author | Grau Sánchez, Miguel |
dc.contributor.author | Grau Gotés, Maria Àngela |
dc.contributor.author | Díaz Barrero, José Luis |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III |
dc.date.accessioned | 2011-05-05T11:25:05Z |
dc.date.available | 2011-05-05T11:25:05Z |
dc.date.issued | 2011-05-02 |
dc.identifier.uri | http://hdl.handle.net/2117/12475 |
dc.description | Report d'un treball de recerca on es presenten noves tècniques de càlcul de l'ordre de convergència amb una aritmètica adaptativa. |
dc.description.abstract | In 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.extent | 14 p. |
dc.language.iso | eng |
dc.rights | Attribution-NonCommercial-NoDerivs 3.0 Spain |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica |
dc.subject.lcsh | Nonlinear systems |
dc.subject.lcsh | Iterative methods (Mathematics) |
dc.subject.lcsh | Numerical analysis |
dc.subject.lcsh | Convergence |
dc.title | On computational order of convergence of some multi-precision solvers of nonlinear systems of equations |
dc.type | External research report |
dc.subject.lemac | Mètodes iteratius (Matemàtica) |
dc.subject.lemac | Anàlisi numèrica |
dc.subject.lemac | Convergència (Matemàtica) |
dc.contributor.group | Universitat Politècnica de Catalunya. NRG - Riscos Naturals i Geoestadística |
dc.contributor.group | Universitat Politècnica de Catalunya. MMAC - Models Matemàtics aplicats a les ciencies humanes i de la natura |
dc.subject.ams | Classificació AMS::65 Numerical analysis::65H Nonlinear algebraic or transcendental equations |
dc.subject.ams | Classificació AMS::41 Approximations and expansions |
dc.rights.access | Open Access |
local.identifier.drac | 5714632 |
dc.description.version | Preprint |
local.personalitzacitacio | true |
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