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Regularization of ill-posed operator equations: an overview
Published in Springer Science and Business Media B.V.
We discuss and illustrate the stability issues associated with ill-posed linear operator equations and the need to have regularization methods for obtaining stable approximate solutions. As illustration, we describe two simple regularization methods, namely, the Lavrentiev regularization in the setting of a Banach spaces and Tikhonov regularization in the setting of Hilbert spaces, and discuss on the corresponding error estimates. We also indicate procedures to obtain error estimates under milder general source conditions and also to obtain better error estimates under modified methods. The discussed procedures include some of the work of the author as well. © 2020, Forum D'Analystes, Chennai.
About the journal
JournalData powered by TypesetJournal of Analysis
PublisherData powered by TypesetSpringer Science and Business Media B.V.
Open AccessNo