L. Jodar, E. Ponsoda, Departamento de Matematica Aplicada., Universidad Politecnica de Valencia, P.O. Box 22.012 Valencia, Spain; G. Rodriguez, Departamento de Estadistica y Matematica Aplicada, E.U.I.T.I. de Bejar, Universidad de Salamanca, 37.700 Bejar, Salamanca, Spain
Abstract: In this paper we propose a procedure to construct approximations of the inverse of a class of ${\cal C}^m$ 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.
Keywords: approximations, inverse mapping, error bounds
Classification (MSC 1991): 26B10, 34G20, 65D30, 15A24
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