Automatic stopping rule for iterative methods in discrete ill-posed problems

DOI10.1007/s40314-014-0174-3zbMath1337.65034OpenAlexW2077994701MaRDI QIDQ747217

Leonardo S. Borges, Maria Cristina C. Cunha, Fermin S. Viloche Bazán

Publication date: 23 October 2015

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

Full work available at URL: https://doi.org/10.1007/s40314-014-0174-3

zbMATH Keywords

regularizationpreconditioningprojection methodill-posed problemstopping ruleKrylov subspace methodgeneralized minimal residual methodparameter choiceleast squares QR-methods

Mathematics Subject Classification ID

Ill-posedness and regularization problems in numerical linear algebra (65F22) Iterative numerical methods for linear systems (65F10) Preconditioners for iterative methods (65F08)

Related Items (6)

Weighted conjugate gradient-type methods for solving quadrature discretization of Fredholm integral equations of the first kind ⋮ A fast adaptive algorithm for nonlinear inverse problems with convex penalty ⋮ Inverse time-dependent source problem for the heat equation with a nonlocal Wentzell-Neumann boundary condition ⋮ Double precision is not necessary for LSQR for solving discrete linear ill-posed problems ⋮ Optimization methods for regularization-based ill-posed problems: a survey and a multi-objective framework ⋮ An iterative method to compute minimum norm solutions of ill-posed problems in Hilbert spaces

Uses Software

• LSQR
• Regularization tools
• corner.m
• CRAIG

Cites Work

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• Implementations of range restricted iterative methods for linear discrete ill-posed problems
• Comparing parameter choice methods for regularization of ill-posed problems
• Invertible smoothing preconditioners for linear discrete ill-posed problems
• The discrete Picard condition for discrete ill-posed problems
• Noise propagation in regularizing iterations for image deblurring
• An improved preconditioned LSQR for discrete ill-posed problems
• Iterative regularization with minimum-residual methods
• Regularization methods for large-scale problems
• Regularization tools: A Matlab package for analysis and solution of discrete ill-posed problems
• GMRES-type methods for inconsistent systems
• A weighted pseudoinverse, generalized singular values, and constrained least squares problems
• The triangle method for finding the corner of the L-curve
• Old and new parameter choice rules for discrete ill-posed problems
• Convergence analysis of minimization-based noise level-free parameter choice rules for linear ill-posed problems
• An adaptive pruning algorithm for the discrete L-curve criterion
• Choosing Regularization Parameters in Iterative Methods for Ill-Posed Problems
• Robust generalized cross-validation for choosing the regularization parameter
• Fixed-point iterations in determining the Tikhonov regularization parameter
• Remarks on choosing a regularization parameter using the quasi-optimality and ratio criterion
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
• Solution of Sparse Indefinite Systems of Linear Equations
• The Use of the L-Curve in the Regularization of Discrete Ill-Posed Problems
• Rank-Deficient and Discrete Ill-Posed Problems
• Bounding the Subspaces from Rank Revealing Two-Sided Orthogonal Decompositions
• A Regularization Parameter in Discrete Ill-Posed Problems
• Discrete Inverse Problems
• A Projection‐Based Approach to General‐Form Tikhonov Regularization
• Smoothing‐Norm Preconditioning for Regularizing Minimum‐Residual Methods
• An Iteration Formula for Fredholm Integral Equations of the First Kind
• Methods of conjugate gradients for solving linear systems

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