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General source conditions for nonlinear ill-posed equations
Published in
2007
Volume: 28
   
Issue: 1-2
Pages: 111 - 126
Abstract
In order to derive error estimates for regularized approximate solutions of ill-posed equations F(x)=y, where F : D(F)XY is a nonlinear operator between Hilbert spaces X and Y, certain source conditions are to be imposed on the unknown solution [image omitted]. For linear ill-posed equations of the form Ax=y, where A:XY is a bounded linear operator, Nair, Schock, and Tautenhahn considered a general source condition, namely, [image omitted]M, :={[(A*A)]1/2v: v}, where the function is general enough to include some of the well-studied special cases. We extend such procedure to the nonlinear ill-posed equations F(x)=y, so that it also includes the results of Tautenhahn where the special case of ():=/2 is considered.
About the journal
JournalNumerical Functional Analysis and Optimization
ISSN01630563
Open AccessNo
Concepts (10)
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    Approximation theory
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    Boundary conditions
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    Functional analysis
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    Hilbert spaces
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    Problem solving
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    GENERAL SOURCE CONDITIONS
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    ILL-POSED EQUATIONS
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    MOROZOV'S DISCREPANCY PRINCIPLE
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    NONLINEAR OPERATOR
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    Nonlinear equations