Journal
NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION
Volume 21, Issue 3-4, Pages 439-464Publisher
MARCEL DEKKER INC
DOI: 10.1080/01630560008816965
Keywords
regularization; ill-posed problems; logarithmic source conditions; modelling errors; backwards heat equation; sideways heat equation
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Linear and nonlinear inverse problems which are exponentially ill-posed arise in heat conduction, satellite gradiometry, potential theory and scattering theory. For these problems logarithmic source conditions have natural interpretations whereas standard Holder-type source conditions are far too restrictive. This paper provides a systematic study of convergence rates of regularization methods under logarithmic source conditions including the case that the operator is given only approximately. We also extend previous convergence results for the iteratively regularized Gau ss-Newton method to operator approximations.
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