Algorithms for range restricted iterative methods for linear discrete ill-posed problems

DOI10.1007/s11075-011-9491-4zbMath1236.65040OpenAlexW1994353272MaRDI QIDQ663490

Arthur Neuman, Lothar Reichel, Hassane Sadok

Publication date: 15 February 2012

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-011-9491-4

zbMATH Keywords

iterative methodArnoldi processtruncated iterationlarge nonsymmetric linear discrete ill-posed problems

Mathematics Subject Classification ID

Ill-posedness and regularization problems in numerical linear algebra (65F22)

Related Items (19)

A stabilized GMRES method for singular and severely ill-conditioned systems of linear equations ⋮ Global Golub-Kahan bidiagonalization applied to large discrete ill-posed problems ⋮ A note on augmented unprojected Krylov subspace methods ⋮ Preconditioned RRGMRES for Discrete Ill-Posed Problems ⋮ On regularizing effects of MINRES and MR-II for large scale symmetric discrete ill-posed problems ⋮ Regularizing preconditioners by non-stationary iterated Tikhonov with general penalty term ⋮ Application of denoising methods to regularizationof ill-posed problems ⋮ An Arnoldi-based preconditioner for iterated Tikhonov regularization ⋮ Range restricted iterative methods for linear discrete ill-posed problems ⋮ Numerical considerations of block GMRES methods when applied to linear discrete ill-posed problems ⋮ Old and new parameter choice rules for discrete ill-posed problems ⋮ Some results on the regularization of LSQR for large-scale discrete ill-posed problems ⋮ FGMRES for linear discrete ill-posed problems ⋮ The structure of iterative methods for symmetric linear discrete ill-posed problems ⋮ Some properties of range restricted GMRES methods ⋮ The sub-Cauchy-Stokes problem: solvability issues and Lagrange multiplier methods with artificial boundary conditions ⋮ The regularizing properties of global GMRES for solving large-scale linear discrete ill-posed problems with several right-hand sides ⋮ Square smoothing regularization matrices with accurate boundary conditions ⋮ rrgmrestbx

Uses Software

• Matlab
• Regularization tools

Cites Work

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• Implementations of range restricted iterative methods for linear discrete ill-posed problems
• Noise propagation in regularizing iterations for image deblurring
• On the regularizing properties of the GMRES method
• Regularization tools version \(4.0\) for matlab \(7.3\)
• Improvement of the resolution of an instrument by numerical solution of an integral equation
• A mollifier method for linear operator equations of the first kind
• Computational Methods for Integral Equations
• A Technique for the Numerical Solution of Certain Integral Equations of the First Kind
• The Use of Auto-correlation for Pseudo-rank Determination in Noisy III-conditioned Linear Least-squares Problems
• Breakdown-free GMRES for Singular Systems

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