On possibility of obtaining linear accuracy evaluation of approximate solutions to inverse problems

DOI10.3103/S1066369X16100042zbMath1370.65029OpenAlexW2525886841MaRDI QIDQ2364399

Alexander S. Leonov

Publication date: 19 July 2017

Published in: Russian Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3103/s1066369x16100042

zbMATH Keywords

regularizationresidual methodill-posed inverse problemslinear a priori estimate of accuracymethod of quasi-solutionswell-posedness in the sense of Tikhonov

Mathematics Subject Classification ID

Nonlinear ill-posed problems (47J06) Numerical solutions to equations with nonlinear operators (65J15) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Numerical solution to inverse problems in abstract spaces (65J22)

Related Items (5)

Solution of ill-posed nonconvex optimization problems with accuracy proportional to the error in input data ⋮ Quasi-solution method and global minimization of the residual functional in conditionally well-posed inverse problems ⋮ On regularization procedures with linear accuracy estimates of approximations ⋮ Ill-Posed Nonlinear Optimization Problems and Uniform Accuracy Estimates of Regularization Methods ⋮ On the achievable level of accuracy for the solution of abstract ill-posed problems and nonlinear operator equations in a Banach space

Cites Work

• Iterative methods of stochastic approximation for solving non-regular nonlinear operator equations
• Can an a priori error estimate for an approximate solution of an ill-posed problem be comparable with the error in data?
• Conditionally well-posed and generalized well-posed problems
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