Equations of the First Kind
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 , Engl, Hanke, and Neubauer , Groetsch , Kirsch , Louis , Morozov , and Tikhonov and Arsenin .
KeywordsRegularization Parameter Compact Operator Bounded Linear Operator Singular System Regularization Scheme
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