Accurate conjugate gradient methods for families of shifted systems

DOI10.1016/j.apnum.2003.11.010zbMath1053.65023OpenAlexW2152831905MaRDI QIDQ1826599

Jasper van den Eshof, Gerard L. G. Sleijpen

Publication date: 6 August 2004

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://dspace.library.uu.nl/handle/1874/16105

zbMATH Keywords

numerical examplesiterative methodsTikhonov regularizationKrylov subspace methodroundoff error analysisconjugate gradient least squares methodfinite precision arithmeticshifted systems

Mathematics Subject Classification ID

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

Related Items (11)

Nested Krylov Methods for Shifted Linear Systems ⋮ BiCR-type methods for families of shifted linear systems ⋮ Flexible and multi-shift induced dimension reduction algorithms for solving large sparse linear systems ⋮ Iterative numerical methods for sampling from high dimensional Gaussian distributions ⋮ Generalized product-type methods based on bi-conjugate gradient (GPBiCG) for solving shifted linear systems ⋮ Solving shifted linear systems with restarted GMRES augmented with error approximations ⋮ An Extension of the COCR Method to Solving Shifted Linear Systems with Complex Symmetric Matrices ⋮ Implementation of a restarted Krylov subspace method for the evaluation of matrix functions ⋮ On restarted and deflated block FOM and GMRES methods for sequences of shifted linear systems ⋮ An efficient and modular grad-div stabilization ⋮ Preconditioner based on the Sherman-Morrison formula for regularized least squares problems

Uses Software

• Regularization tools
• BiCGstab

Cites Work

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• BiCGStab(\(\ell\)) for families of shifted linear systems
• Arnoldi methods for large Sylvester-like observer matrix equations, and an associated algorithm for partial spectrum assignment
• Behavior of slightly perturbed Lanczos and conjugate-gradient recurrences
• Regularization tools: A Matlab package for analysis and solution of discrete ill-posed problems
• Restarted full orthogonalization method for shifted linear systems
• Perturbation identities for regularized Tikhonov inverses and weighted pseudo- inverses
• On error estimation in the conjugate gradient method and why it works in finite precision computations
• A Symmetric Band Lanczos Process Based on Coupled Recurrences and Some Applications
• On the Numerical Solution of $(\lambda^2 A + \lambda B + C), x = b$ and Application to Structural Dynamics
• Error Analysis of the Lanczos Algorithm for Tridiagonalizing a Symmetric Matrix
• Fast CG-Based Methods for Tikhonov--Phillips Regularization
• An Implementation of the QMR Method Based on Coupled Two-Term Recurrences
• Estimating the Attainable Accuracy of Recursively Computed Residual Methods
• Stability of Conjugate Gradient and Lanczos Methods for Linear Least Squares Problems
• Restarted GMRES for Shifted Linear Systems
• A Unified Theoryof Conditioning for Linear Least Squares and Tikhonov Regularization Solutions
• Methods of conjugate gradients for solving linear systems

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