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arXiv · 0707.0505

Deflated Iterative Methods for Linear Equations with Multiple Right-Hand Sides

Ronald B. Morgan·Walter Wilcox
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Abstract

A new approach is discussed for solving large nonsymmetric systems of linear equations with multiple right-hand sides. The first system is solved with a deflated GMRES method that generates eigenvector information at the same time that the linear equations are solved. Subsequent systems are solved by combining restarted GMRES with a projection over the previously determined eigenvectors. This approach offers an alternative to block methods, and it can also be combined with a block method. It is useful when there are a limited number of small eigenvalues that slow the convergence. An example is given showing significant improvement for a problem from quantum chromodynamics. The second and subsequent right-hand sides are solved much quicker than without the deflation. This new approach is relatively simple to implement and is very efficient compared to other deflation methods.

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Ronald B. Morgan, Walter Wilcox. 2007-07-03. Deflated Iterative Methods for Linear Equations with Multiple Right-Hand Sides. https://arxiv.org/abs/0707.0505

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