Multiscale analysis for ill-posed problems with semi-discrete Tikhonov regularization

DOI10.1088/0266-5611/28/6/065019zbMath1254.65071OpenAlexW2024524509MaRDI QIDQ2898435

Min Zhong, Jin Cheng, Shuai Lu

Publication date: 11 July 2012

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

Full work available at URL: https://doi.org/10.1088/0266-5611/28/6/065019

zbMATH Keywords

algorithmerror estimatesnumerical examplesHilbert spaceintegral operatorTikhonov regularizationlinear ill-posed problemsmultiscale analysisMorozov's discrepancy principlelinear inverse problemSobolev functionsill-posed linear operator equationsdiscrete noisy datamoderate ill-posedness

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) 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)

Related Items (8)

Semi-discrete Tikhonov regularization in RKHS with large randomly distributed noise ⋮ A multiscale RBF method for severely ill-posed problems on spheres ⋮ Regularization method for the generalized moment problem in a functional reproducing kernel Hilbert space ⋮ A multiscale support vector regression method on spheres with data compression ⋮ Regularization in a functional reproducing kernel Hilbert space ⋮ Tikhonov regularization for polynomial approximation problems in Gauss quadrature points ⋮ Multiscale support vector approach for solving ill-posed problems ⋮ Multiscale support vector regression method in Sobolev spaces on bounded domains

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