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Error estimation for ill-posed problems on piecewise convex functions and sourcewise represented sets.
- Source :
- Journal of Inverse & Ill-Posed Problems; 2008, Vol. 16 Issue 6, p625-638, 14p
- Publication Year :
- 2008
-
Abstract
- In this paper solutions of ill-posed problems with some a priori information about the exact solution are considered. For the first group of such problems it is supposed that the exact solution is a bounded piecewise convex function on some bounded segment [ a, b]. It is shown that the set of these functions is a compact set in L<superscript>P</superscript>[ a, b] and an approximate solution tends to the exact one uniformly on some subset of [ a, b]. Sourcewise represented functions form the second group of the problems. For this case it is possible to find a so-called a posteriori error estimation of an approximate solution. The method of extending compacts may help to estimate this a posteriori error. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 09280219
- Volume :
- 16
- Issue :
- 6
- Database :
- Complementary Index
- Journal :
- Journal of Inverse & Ill-Posed Problems
- Publication Type :
- Academic Journal
- Accession number :
- 47102137
- Full Text :
- https://doi.org/10.1515/JIIP.2008.034