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V. N. Titarenko, A. G. Yagola
The problems of linear and quadratic programming for ill-posed problems on some compact sets
In this paper the problem of finding the error of an approximate solution for ill-posed problems on some compact sets is discussed. Sets of bounded monotonic or convex functions and sets of functions with a given Lipschitz constant are considered. These functions are given on a segment. Two approaches are used to construct sets of approximate solutions. In the first approach we assume that a function for the right-hand side of an operator equation is given on the whole segment. In the second approach we use only grid values of this function. Applying these approaches, we obtain quadratic or linear programming problems and find functions bounding above and below these approximate solutions. In the paper we use two algorithms to find errors that determine the sets of approximate solutions for the cases when operators of the problems are positive or integral. The inverse problem for the heat conduction equation is considered as a model example.
Journal of Inverse and Ill-posed Problems, Walter de Gruyter
Print ISSN: 0928-0219
Volume: 11, 09/2003
Pages: 311 - 328