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Approximations and error bounds for computing the inverse mapping

Lucas Jódar, Enrique Ponsoda, G. Rodríguez Sánchez (1997)

Applications of Mathematics

In this paper we propose a procedure to construct approximations of the inverse of a class of 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.

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