A polynomial preconditioner for the GMRES algorithm

DOI10.1016/0377-0427(94)00015-SzbMath0831.65033OpenAlexW2137797529MaRDI QIDQ1899971

Martin B. van Gijzen

Publication date: 18 February 1996

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

Full work available at URL: https://doi.org/10.1016/0377-0427(94)00015-s

zbMATH Keywords

numerical experimentseigenvalue estimatesGMRES algorithmnonsymmetric linear systemspolynomial preconditioner

Mathematics Subject Classification ID

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

Related Items

An efficient two-level preconditioner for multi-frequency wave propagation problems, GMRES convergence bounds for eigenvalue problems, Matrix-free polynomial-based nonlinear least squares optimized preconditioning and its application to discontinuous Galerkin discretizations of the Euler equations, Large scale finite element computations with GMRES-like methods on a Cray Y-MP, Restarted GMRES preconditioned by deflation, Parallel matrix-free polynomial preconditioners with application to flow simulations in discrete fracture networks, GMRES algorithms over 35 years, On the convergence of Krylov methods with low-rank truncations, A polynomial preconditioner for the CMRH algorithm, Preconditioning the Helmholtz equation with the shifted Laplacian and Faber polynomials, Preconditioned Multishift BiCG for $\mathcal{H}_2$-Optimal Model Reduction

Uses Software

• CGS

Cites Work

• An optimum iterative method for solving any linear system with a square matrix
• The Tchebychev iteration for nonsymmetric linear systems
• The superlinear convergence behaviour of GMRES
• Mathematical modelling of the cardiovascular system
• An analysis of element-by-element preconditioners for nonsymmetric problems
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• Least Squares Polynomials in the Complex Plane and Their Use for Solving Nonsymmetric Linear Systems
• CGS, A Fast Lanczos-Type Solver for Nonsymmetric Linear systems
• Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
• A Hybrid GMRES Algorithm for Nonsymmetric Linear Systems
• A Hybrid Chebyshev Krylov Subspace Algorithm for Solving Nonsymmetric Systems of Linear Equations
• The principle of minimized iterations in the solution of the matrix eigenvalue problem
• Methods of conjugate gradients for solving linear systems
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