On the convergence rate of the conjugate gradients in presence of rounding errors

DOI10.1007/BF01385754zbMath0791.65016MaRDI QIDQ1326451

Yvan Notay

Publication date: 7 July 1994

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/133737

zbMATH Keywords

preconditioningiterative methodconvergence rateconjugate gradientsacceleration of convergencerounding errorsnumber of iterations

Mathematics Subject Classification ID

Iterative numerical methods for linear systems (65F10) Roundoff error (65G50) Numerical computation of matrix norms, conditioning, scaling (65F35)

Related Items

Estimates in quadratic formulas, Hierarchical matrix approximation with blockwise constraints, Error norm estimation and stopping criteria in preconditioned conjugate gradient iterations, Spectral analysis of parallel incomplete factorizations with implicit pseudo‐overlap, Total and selective reuse of Krylov subspaces for the resolution of sequences of nonlinear structural problems, Explicit approximate inverse preconditioning techniques, Analyzing the Effect of Local Rounding Error Propagation on the Maximal Attainable Accuracy of the Pipelined Conjugate Gradient Method, Composite convergence bounds based on Chebyshev polynomials and finite precision conjugate gradient computations, ON THE RATE OF CONVERGENCE AND COMPLEXITY OF NORMALIZED IMPLICIT PRECONDITIONING FOR SOLVING FINITE DIFFERENCE EQUATIONS IN THREE SPACE VARIABLES, Scaling, reordering, and diagonal pivoting in ILU preconditionings, Milestones in the development of iterative solution methods, Applications of statistical condition estimation to the solution of linear systems, A performance study of normalized explicit finite element approximate inverse preconditioning on uniprocessor and multicomputer systems, Data assimilation in weather forecasting: a case study in PDE-constrained optimization, Numerical methods and algorithms. Part XIII, Analysis of the finite precision bi-conjugate gradient algorithm for nonsymmetric linear systems, Iteration number for the conjugate gradient method

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the real convergence rate of the conjugate gradient method
• On the rate of convergence of the preconditioned conjugate gradient method
• The rate of convergence of conjugate gradients
• Behavior of slightly perturbed Lanczos and conjugate-gradient recurrences
• A class of iterative methods for finite element equations
• Predicting the Behavior of Finite Precision Lanczos and Conjugate Gradient Computations
• Influence of the Eigenvalue Spectrum on the Convergence Rate of the Conjugate Gradient Method
• Methods of conjugate gradients for solving linear systems