Minimal polynomial and reduced rank extrapolation methods are related

DOI10.1007/s10444-016-9481-0zbMath1370.65025arXiv1503.02552OpenAlexW2964031827MaRDI QIDQ2361155

Avram Sidi

Publication date: 29 June 2017

Published in: Advances in Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1503.02552

zbMATH Keywords

convergence accelerationKrylov subspace methodsminimal polynomial extrapolationvector extrapolation methodsreduced rank extrapolationmethod of Arnoldimethod of generalized minimal residuals

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Numerical computation of solutions to systems of equations (65H10) Extrapolation to the limit, deferred corrections (65B05) Iterative numerical methods for linear systems (65F10) General theory of numerical methods in complex analysis (potential theory, etc.) (65E05)

Related Items

A convergence study for reduced rank extrapolation on nonlinear systems ⋮ The genesis and early developments of Aitken's process, Shanks' transformation, the \(\varepsilon\)-algorithm, and related fixed point methods

Cites Work

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• Some observations on weighted GMRES
• Convergence and stability analyses for some vector extrapolation methods in the presence of defective iteration matrices
• Extrapolation vs. projection methods for linear systems of equations
• Recursive algorithms for vector extrapolation methods
• Conjugate gradient type methods for unsymmetric and inconsistent systems of linear equations
• Generalized conjugate-gradient acceleration of nonsymmetrizable iterative methods
• Efficient implementation of minimal polynomial and reduced rank extrapolation methods
• Extrapolation methods theory and practice
• Convergence acceleration for the iterative solution of the equations X = AX + f
• Upper bounds for convergence rates of acceleration methods with initial iterations
• Weighted FOM and GMRES for solving nonsymmetric linear systems
• Convergence of intermediate rows of minimal polynomial and reduced rank extrapolation tables
• On the modified Gram-Schmidt algorithm for weighted and constrained linear least squares problems
• Residual smoothing and peak/plateau behavior in Krylov subspace methods
• Least-square acceleration of iterative methods for linear equations
• Variational Iterative Methods for Nonsymmetric Systems of Linear Equations
• Geometric aspects of the theory of Krylov subspace methods
• Acceleration of Convergence of Vector Sequences
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• Convergence and Stability Properties of Minimal Polynomial and Reduced Rank Extrapolation Algorithms
• Extrapolation Methods for Vector Sequences
• Krylov Subspace Methods for Solving Large Unsymmetric Linear Systems
• Modifying the QR-Decomposition to Constrained and Weighted Linear Least Squares
• Changing the Norm in Conjugate Gradient Type Algorithms
• A Polynomial Extrapolation Method for Finding Limits and Antilimits of Vector Sequences
• Residual Smoothing Techniques for Iterative Methods
• Properties of generalized conjugate gradient methods
• Iterative Krylov Methods for Large Linear Systems
• Relations between Galerkin and Norm-Minimizing Iterative Methods for Solving Linear Systems
• A Theoretical Comparison of the Arnoldi and GMRES Algorithms
• The principle of minimized iterations in the solution of the matrix eigenvalue problem