Equations of the First Kind

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


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].


Regularization Parameter Compact Operator Bounded Linear Operator Singular System Regularization Scheme 
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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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