Geodesic
Approximations and error bounds for computing the inverse mapping
Applications of Mathematics, Tome 42 (1997) no. 2, pp. 99-110

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In this paper we propose a procedure to construct approximations of the inverse of a class of ${\mathcal C}^{m}$ 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.
DOI : 10.1023/A:1022291010828
Classification : 15A24, 26B10, 34A45, 34G20, 65D15, 65D30, 65H10, 65L06
Keywords: approximations; inverse mapping; error bounds; Banach space; matrix differential equations; one-step-method; numerical example 
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Jódar, L.; Ponsoda, E.; Rodríguez, G. Approximations and error bounds for computing the inverse mapping. Applications of Mathematics, Tome 42 (1997) no. 2, pp. 99-110. doi: 10.1023/A:1022291010828

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