Journal of Inverse and Ill-posed Problems
Editor-in-Chief: Kabanikhin, Sergey I.
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Necessary and sufficient conditions for logarithmic convergence of regularization methods for solving inverse Cauchy problem in Banach space
∗Mary State University, 424001, Yoshkar-Ola, Russia. E-mail: (email)
Citation Information: Journal of Inverse and Ill-posed Problems jiip. Volume 14, Issue 5, Pages 481–504, ISSN (Online) 1569-3953, ISSN (Print) 0928-0219, DOI: 10.1515/156939406778247606,
- Published Online:
We consider an abstract inverse Cauchy problem with a sectorial operator A in a Banach space. For solving the problem, a class of regularization methods is used and their rate of convergence is studied in terms of the regularization parameter α → 0+. It is shown that the methods provide an approximation error of order O((– ln α)−p) (p > 0) if and only if the initial discrepancy has a sourcewise representation with respect to the operator A−p.