Approximate Solutions to Integral Equations by Wavelet Decomposition Methods

María I. Troparevsky, Eduardo P. Serrano, Marcela A. Fabio


We construct approximate solutions to Inverse Problems associated to equations of the form Af = g where A is an integral operator. For a given f , the Forward Problem consists in calculating its image through A, while the Inverse Problem looks for f for a given g. In order to solve the Inverse Problem we project the data into finite dimensional subspaces of wavelets in the context of a multiresolution analysis and solve the Foward Problem for each element of the basis by means of a Galerkin-type scheme. From these computations, we can accurately build a solution to the Inverse Problem based on properties of the chosen wavelets and suitable hyphotesis on the operator. We present examples related to fractional calculus.

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