On computing quadrature-based bounds for the \(A\)-norm of the error in conjugate gradients
type: Item
instance of: scholarly article
title: On computing quadrature-based bounds for the \(A\)-norm of the error in conjugate gradients
zbMATH Open document ID: 1261.65034
author: Petr Tichý
author: G. Meurant
published in: Numerical Algorithms
publication date: 2013-02-15T00:00:00Z
review text: The authors use the fact that the conjugate gradient method computes the Cholesky decomposition of the Jacobi matrix which is given implicitly. The authors directly compute the entries of the Cholesky decompositions of the modified Jacobi matrices for the Gauss-Radau and Gauss-Lobatto quadratures.
reviewed by: Răzvan Răducanu
Mathematics Subject Classification ID: 65F10
zbMATH DE Number: 6136616
zbMATH Keywords: conjugate gradient
zbMATH Keywords: norm of error
zbMATH Keywords: bounds of error norm
zbMATH Keywords: Cholesky decomposition
zbMATH Keywords: Jacobi matrix
zbMATH Keywords: Gauss-Radau and Gauss-Lobatto quadratures
describes a project that uses: OPQ
MaRDI profile type: Publication
full work available at URL: s11075-012-9591-9
OpenAlex ID: W2008296506
cites work: A stopping criterion for the conjugate gradient algorithm in a finite element method framework
cites work: Approximation of the roots of equations by Aitken-Steffensen-type monotonic sequences
cites work: Error Estimates for the Solution of Linear Systems
cites work: Computable error bounds and estimates for the conjugate gradient method
cites work: An iterative method with error estimators
cites work: Bounds for the error of linear systems of equations using the theory of moments
cites work: Q3207994
cites work: Q4309408
cites work: Q4820343
cites work: Some Modified Matrix Eigenvalue Problems
cites work: Q4288554
cites work: Matrices, moments and quadrature. II: How to compute the norm of the error iterative methods
cites work: Q5851422
cites work: Estimates in quadratic formulas
cites work: Q5689624
cites work: Calculation of Gauss Quadrature Rules
cites work: Methods of conjugate gradients for solving linear systems
cites work: A Posteriori Error Estimates Including Algebraic Error and Stopping Criteria for Iterative Solvers
cites work: Anti-Gaussian quadrature formulas
cites work: The computation of bounds for the norm of the error in the conjugate gradient algorithm
cites work: Numerical experiments in computing bounds for the norm of the error in the preconditioned conjugate gradient algorithm
cites work: The Lanczos and Conjugate Gradient Algorithms
cites work: The Lanczos and conjugate gradient algorithms in finite precision arithmetic
cites work: Q4840770
cites work: Relatively robust representations of symmetric tridiagonals
cites work: Q4779819
cites work: On error estimation in the conjugate gradient method and why it works in finite precision computations
cites work: Error estimation in preconditioned conjugate gradients
cites work: Q3290777
DOI: 10.1007/S11075-012-9591-9
description: scientific article; zbMATH DE number 6136616