Convergence rates for Tikhonov regularization based on range inclusions

DOI10.1088/0266-5611/21/3/002zbMath1077.65056OpenAlexW2083642275MaRDI QIDQ5462069

Bernd Hofmann, Masahiro Yamamoto

Publication date: 1 August 2005

Published in: Inverse Problems (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/338a84bd3076b69cf649d7fd212ea529595a2da4

zbMATH Keywords

inverse problemsHilbert spacesAbel integral equationlinear ill-posed problemsTikhonov's regularization method

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Inverse problems for PDEs (35R30) Numerical solutions to equations with linear operators (65J10) Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) (45E10) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs (65M32) Linear operators and ill-posed problems, regularization (47A52)

Related Items (12)

On the analysis of distance functions for linear ill-posed problems with an application to the integration operator inL² ⋮ Padé iteration method for regularization ⋮ Variational multiscale nonparametric regression: smooth functions ⋮ Range inclusion of operators on non-archimedean Banach space ⋮ The residual method for regularizing ill-posed problems ⋮ Impact of conditional stability: Convergence rates for general linear regularization methods ⋮ Big in Japan: regularizing networks for solving inverse problems ⋮ Regularization by projection: Approximation theoretic aspects and distance functions ⋮ Range Inclusions and Approximate Source Conditions with General Benchmark Functions ⋮ Direct and inverse results in variable Hilbert scales ⋮ Regularization by projection in variable Hilbert scales ⋮ Convergence rates for Tikhonov regularization from different kinds of smoothness conditions

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