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Pré-Publication, Document De Travail Année : 2018

A PROJECTION BASED REGULARIZED APPROXIMATION METHOD FOR ILL-POSED OPERATOR EQUATIONS

Résumé

Problem of solving Fredholm integral equations of the first kind is a prototype of an ill-posed problem of the form T (x) = y, where T is a compact operator between Hilbert spaces. Regularizations and discretizations of such equations are necessary for obtaining stable approximate solutions for such problems. For ill-posed integral equations, a quadrature based collocation method has been considered by Nair (2012) for obtaining discrete regularized approximations. As a generalization of that, a projection collocation method has been studied in 2016. In both of the considered methods, the operator T is approximate by a sequence of finite rank operators. In the present paper, the authors choose to approximate T T * by finite rank operators. It is found that in some cases, the derived estimates are improvements over the previous estmiates.
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Dates et versions

hal-01782310 , version 1 (01-05-2018)

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Domaine public

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  • HAL Id : hal-01782310 , version 1

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Laurence Grammont, M T Nair. A PROJECTION BASED REGULARIZED APPROXIMATION METHOD FOR ILL-POSED OPERATOR EQUATIONS. 2018. ⟨hal-01782310⟩
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