Conditions for the qualified convergence of finite difference methods and the quasi-reversibility method for solving linear ill-posed Cauchy problems in a Hilbert space

DOI10.3103/S1066369X19100062zbMath1445.47012OpenAlexW2986993177MaRDI QIDQ2191539

Mikhail M. Kokurin

Publication date: 25 June 2020

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

Full work available at URL: https://doi.org/10.3103/s1066369x19100062

zbMATH Keywords

convergenceabstract Cauchy problemHilbert spacefinite difference methodsill-posed problemconverse theoremsquasi-reversibity method

Mathematics Subject Classification ID

Ill-posed problems for PDEs (35R25) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Linear operators and ill-posed problems, regularization (47A52)

Related Items (1)

Direct and converse theorems for iterative methods of solving irregular operator equations and finite difference methods for solving ill-posed Cauchy problems

Cites Work

• Necessary and sufficient conditions for the polynomial convergence of the quasi-reversibility and finite-difference methods for an ill-posed Cauchy problem with exact data
• The functional calculus for sectorial operators
• Numerical methods for solving inverse problems of mathematical physics.
• On a class of finite-difference schemes for solving ill-posed Cauchy problems in Banach spaces
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