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Algorithms for the approximate solution of ill-posed problems on special sets

  • A. N. Tikhonov
  • A. V. Goncharsky
  • V. V. Stepanov
  • A. G. Yagola
Chapter
Part of the Mathematics and Its Applications book series (MAIA, volume 328)

Abstract

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?

Keywords

Exact Solution Approximate Solution Conjugate Gradient Active Constraint Convex Polyhedron 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 1995

Authors and Affiliations

  • A. N. Tikhonov
    • 1
  • A. V. Goncharsky
    • 1
  • V. V. Stepanov
    • 1
  • A. G. Yagola
    • 1
  1. 1.Moscow State UniversityMoscowRussia

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