Approximation accuracy of the Krylov subspaces for linear discrete ill-posed problems

DOI10.1016/j.cam.2020.112786zbMath1434.65043arXiv1805.10132OpenAlexW2803610866MaRDI QIDQ2306411

Zhongxiao Jia

Publication date: 23 March 2020

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1805.10132

zbMATH Keywords

Ritz valuesLanczos bidiagonalizationKrylov subspacediscrete ill-posed problemsemi-convergencefull regularizationpartial regularization

Mathematics Subject Classification ID

Numerical solutions to overdetermined systems, pseudoinverses (65F20) Ill-posedness and regularization problems in numerical linear algebra (65F22) Inverse problems in geophysics (86A22) Eigenvalues, singular values, and eigenvectors (15A18) Inverse problems in linear algebra (15A29) Iterative numerical methods for linear systems (65F10) Numerical methods for ill-posed problems for integral equations (65R30) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Numerical methods for inverse problems for integral equations (65R32) Linear operators and ill-posed problems, regularization (47A52) Inverse problems for integral equations (45Q05) Numerical solution to inverse problems in abstract spaces (65J22)

Related Items (7)

Regularization properties of Krylov iterative solvers CGME and LSMR for linear discrete ill-posed problems with an application to truncated randomized SVDs ⋮ A joint bidiagonalization based iterative algorithm for large scale general-form Tikhonov regularization ⋮ Krylov methods for inverse problems: Surveying classical, and introducing new, algorithmic approaches ⋮ A CCBM-based generalized GKB iterative regularization algorithm for inverse Cauchy problems ⋮ Regularization properties of LSQR for linear discrete ill-posed problems in the multiple singular value case and best, near best and general low rank approximations ⋮ The low rank approximations and Ritz values in LSQR for linear discrete ill-posed problem ⋮ Sinc Collocation Numerical Methods for Solving Two-Dimensional Gross-Pitaevskii Equations with Non-Homogeneous Dirichlet Boundary Conditions

Uses Software

• LSQR
• Regularization tools
• GKB-FP
• JDQR
• RestoreTools
• UTV
• JDQZ
• LSMR
• IR Tools
• CRAIG

Cites Work

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