1995 | OriginalPaper | Chapter
Algorithms for the approximate solution of ill-posed problems on special sets
Authors : A. N. Tikhonov, A. V. Goncharsky, V. V. Stepanov, A. G. Yagola
Published in: Numerical Methods for the Solution of Ill-Posed Problems
Publisher: Springer Netherlands
Included in: Professional Book Archive
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In Chapter 2 we have succeeded in solving, in a number of cases, the first problem posed to us: starting from qualitative information regarding the unknown solution, how to find the compact set of well-posedness M containing the exact solution. It was shown that this can be readily done if the exact solution of the problem belongs to Z↓ C , Ž C , Ž↓ C . A uniform approximation to the exact solution of the problem can be constructed if the exact solution is a continuous function of bounded variation. We now turn to the second problem: how to construct an efficient numerical algorithm for solving ill-posed problems on the sets listed above?