文章基本信息

标题：Approximate Solutions to Integral Equations by Wavelet Decomposition Methods
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作者：María I. Troparevsky ; Eduardo P. Serrano ; Marcela A. Fabio 等
期刊名称：Mecánica Computacional
印刷版ISSN：2591-3522
出版年度：2016
卷号：34
期号：50
页码：3383-3394
语种：English
出版社：CIMEC-INTEC-CONICET-UNL
其他摘要：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.