On pseudo—optimal parameter choices and stopping rules for regularization methods in banach spaces∗

DOI10.1080/01630569608816690zbMath0865.65039OpenAlexW1505050097MaRDI QIDQ4886623

Uno Hämarik, Robert Plato

Publication date: 10 July 1997

Published in: Numerical Functional Analysis and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/01630569608816690

zbMATH Keywords

Banach spacesiterative methodsdiscrepancy principleregularization methodsstopping rulesRichardson iterationpseudo-optimal parameter choices

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Numerical solutions to equations with linear operators (65J10) Equations and inequalities involving linear operators, with vector unknowns (47A50) Numerical methods for ill-posed problems for integral equations (65R30) Fredholm integral equations (45B05) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20)

Related Items (8)

The Galerkin scheme for Lavrentiev's \(m\)-times iterated method to solve linear accretive Volterra integral equations of the first kind ⋮ Converse Results, Saturation and Quasi-optimality for Lavrentiev Regularization of Accretive Problems ⋮ Solving large-scale constrained least-squares problems. ⋮ Convergence rates for Kaczmarz-type regularization methods ⋮ A discrete scheme of Landweber iteration for solving nonlinear ill-posed problems ⋮ Ill-posed problems, \(C_{0}\)-semigroups and the Showalter regularization ⋮ Use of extrapolation in regularization methods ⋮ On the iteratively regularized Gauss-Newton method for solving nonlinear ill-posed problems

Cites Work

• Semigroups of linear operators and applications to partial differential equations
• A posteriori parameter choice for general regularization methods for solving linear ill-posed problems
• Resolvent estimates for Abel integral operators and the regularization of associated first kind integral equations
• On the discrepancy principle for iterative and parametric methods to solve linear ill-posed equations
• An a posteriori parameter choice for ordinary and iterated Tikhonov regularization of ill-posed problems leading to optimal convergence rates
• Inner, outer, and generalized inverses in banach and hilbert spaces

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