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Equations of the First Kind

  • Rainer Kress
Part of the Applied Mathematical Sciences book series (AMS, volume 82)

Abstract

Compact operators cannot have a bounded inverse. Therefore, equations of the first kind with a compact operator provide a typical example for socalled ill-posed problems.In this chapter we introduce regularization methods for the stable solution of equations of the first kind in a Hilbert space setting. For a more comprehensive study of ill-posed problems, we refer to Baumeister [13], Engl, Hanke, and Neubauer [38], Groetsch [58], Kirsch [87], Louis [116], Morozov [129], and Tikhonov and Arsenin [174].

Keywords

Regularization Parameter Compact Operator Bounded Linear Operator Singular System Regularization Scheme 
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 New York 1999

Authors and Affiliations

  • Rainer Kress
    • 1
  1. 1.Institut für Numerische und Angewandte MathematikUniversität GöttingenGöttingenGermany

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