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A PROJECTION BASED REGULARIZED APPROXIMATION METHOD FOR ILL-POSED OPERATOR EQUATIONS
| Content Provider | Hyper Articles en Ligne (HAL) |
|---|---|
| Author | Grammont, Laurence Nair, M, T |
| Abstract | 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. |
| Related Links | https://hal.science/hal-01782310/file/Grammont-Nair-300418.pdf |
| Language | English |
| Publisher | HAL CCSD |
| Access Restriction | Open |
| Subject Keyword | Ill-posed prob- lems Projection First kind Fredholm integral equations Inverse problems Tikhonov regularization |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
