Approximations and error bounds for computing the inverse mapping |
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| Authors: | L. Jódar E. Ponsoda G. Rodríguez |
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| Affiliation: | (1) Departamento de Matemática Aplicada., Universidad Politécnica de Valencia, P.O. Box 22.012, Valencia, Spain;(2) Departamento de Estadística y Matemática Aplicada, E.U.I.T.I. de Béjar, Universidad de Salamanca, 37.700 Béjar, Salamanca, Spain |
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| Abstract: | In this paper we propose a procedure to construct approximations of the inverse of a class of Cm differentiable mappings. First of all we determine in terms of the data a neighbourhood where the inverse mapping is well defined. Then it is proved that the theoretical inverse can be expressed in terms of the solution of a differential equation depending on parameters. Finally, using one-step matrix methods we construct approximate inverse mappings of a prescribed accuracy. |
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| Keywords: | approximations inverse mapping error bounds |
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