Error estimation for ill-posed problems on piecewise convex functions and sourcewise represented sets

V. Titarenko, A. Yagola

    Research output: Contribution to journalArticlepeer-review

    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 LPa, 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. © de Gruyter 2008.
    Original languageEnglish
    Pages (from-to)625-638
    Number of pages13
    JournalJournal of Inverse and Ill-Posed Problems
    Volume16
    Issue number6
    DOIs
    Publication statusPublished - Oct 2008

    Keywords

    • Compact set
    • Error estimation
    • Ill-posed problem
    • Method of extending compacts
    • Regularizing algorithm

    Fingerprint

    Dive into the research topics of 'Error estimation for ill-posed problems on piecewise convex functions and sourcewise represented sets'. Together they form a unique fingerprint.

    Cite this