Analytical and numerical studies on the influence of multiplication operators for the ill-posedness of inverse problems

DOI10.1515/1569394053978524zbMath1083.65054OpenAlexW2127713908MaRDI QIDQ5316234

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Publication date: 12 September 2005

Published in: Journal of Inverse and Ill-posed Problems (Search for Journal in Brave)

Full work available at URL: http://opus.bath.ac.uk/25301/3/endversion.pdf

zbMATH Keywords

inverse problemscompact operatorTikhonov regularizationill-posed problemlinear operator equationsNemytskij operatormultiplication operators

Mathematics Subject Classification ID

Numerical solutions to equations with linear operators (65J10) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Linear operators and ill-posed problems, regularization (47A52) Numerical solution to inverse problems in abstract spaces (65J22)

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Cites Work

• Singular values and condition numbers of Galerkin matrices arising from linear integral equations of the first kind
• Computation of the singular value expansion
• On ill-posedness measures and space change in Sobolev scales
• Eigenvalues of Positive Definite Kernels II
• Convergence rates for Tikhonov regularisation of non-linear ill-posed problems
• Asymptotics of singular values of fractional integral operators
• Factors influencing the ill-posedness of nonlinear problems
• Tikhonov regularization for electrical impedance tomography on unbounded domains
• On the nature of ill-posedness of an inverse problem arising in option pricing
• Some results and a conjecture on the degree of ill-posedness for integration operators with weights
• Linear integral equations
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