A projection based regularized approximation method for ill-posed operator equations

The 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. Regularization and discretization of such equations is 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, a projection collocation method has been proposed by the author in 2016. In both of the considered methods, the operator $T$ is approximate by a sequence off infinite rank operators. In the present work, we approximate $TT^\ast$ by finite rank operators. It is found that there are cases where this approach can be better. 

Date and Venue

Start Date
FCUP, Dep. Matemática, anfiteatro FC1 030
End Date


Laurence Grammont

Speaker's Institution

Institut Camille Jordan, Université de Lyon, FRANCE


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