Abstract:
A general approach to modification of well-known methods for the solution of linear ill-posed problems is proposed. The approach enables us to exclude a possible “saturation of accuracy” of methods on classes of sourcewise representable solutions. As a result, the modified methods possess the optimal order of accuracy on each of these classes. Numerical examples for the solution of 1D and 2D inverse problems are presented.
This publication is cited in the following 6 articles:
A. S. Leonov, “Extra-optimal methods for solving ill-posed problems: survey of theory and examples”, Comput. Math. Math. Phys., 60:6 (2020), 960–986
Smirnova A., Bakushinsky A., DeCamp L., “on Application of Asymptotic Generalized Discrepancy Principle To the Analysis of Epidemiology Models”, Appl. Anal., 94:4 (2015), 672–693
A. S. Leonov, “A posteriori accuracy estimations of solutions of ill-posed inverse problems and extra-optimal regularizing algorithms for their solution”, Num. Anal. Appl., 5:1 (2012), 68–83
Leonov A.S., “Extra-Optimal Methods for Solving Ill-Posed Problems”, J. Inverse Ill-Posed Probl., 20:5-6 (2012), 637–665
Mazzieri G.L., Spies R.D., Temperini K.G., “On the Existence of Global Saturation for Spectral Regularization Methods with Optimal Qualification”, J. Inverse Ill-Posed Probl., 20:5-6 (2012), 765–789
Leonov A.S., “Extraoptimal a posteriori estimates of the solution accuracy in the ill-posed problems of the continuation of potential geophysical fields”, Izvestiya Physics of the Solid Earth, 47:6 (2011), 531–540
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