Adaptively Preconditioned GMRES Algorithms

Authors:
J. Baglama;D. Calvetti;G. H. Golub;L. Reichel
Affiliations:
-;-;-;-
Venue:
SIAM Journal on Scientific Computing
Year:
1998

Citing 0
Cited 17

On efficient preconditioners for iterative solution of a Galerkin boundary element equation for the three-dimensional exterior Helmholtz problem

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Restarted block-GMRES with deflation of eigenvalues

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Incremental spectral preconditioners for sequences of linear systems

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Preconditioner updates applied to CFD model problems

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Improving Triangular Preconditioner Updates for Nonsymmetric Linear Systems

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Restarted block-GMRES with deflation of eigenvalues

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VECPAR'02 Proceedings of the 5th international conference on High performance computing for computational science
Deflated and Restarted Symmetric Lanczos Methods for Eigenvalues and Linear Equations with Multiple Right-Hand Sides

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GMRES with adaptively deflated restarting and its performance on an electromagnetic cavity problem

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Novel Numerical Methods for Solving the Time-Space Fractional Diffusion Equation in Two Dimensions

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Flexible Variants of Block Restarted GMRES Methods with Application to Geophysics

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A Flexible Generalized Conjugate Residual Method with Inner Orthogonalization and Deflated Restarting

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Matrix-free continuation of limit cycles for bifurcation analysis of large thermoacoustic systems

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Accelerated GCRO-DR method for solving sequences of systems of linear equations

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Two-level algebraic domain decomposition preconditioners using Jacobi-Schwarz smoother and adaptive coarse grid corrections

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Preconditioning Newton---Krylov methods in nonconvex large scale optimization

Computational Optimization and Applications

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Abstract

The restarted GMRES algorithm proposed by Saad and Schultz [SIAM J. Sci. Statist. Comput., 7 (1986), pp. 856--869] is one of the most popular iterative methods for the solution of large linear systems of equations Ax=b with a nonsymmetric and sparse matrix. This algorithm is particularly attractive when a good preconditioner is available. The present paper describes two new methods for determining preconditioners from spectral information gathered by the Arnoldi process during iterations by the restarted GMRES algorithm. These methods seek to determine an invariant subspace of the matrix A associated with eigenvalues close to the origin and to move these eigenvalues so that a higher rate of convergence of the iterative methods is achieved.