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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 an iterative method with a projection over the previously determined eigenvectors. Restarted GMRES is considered for the iterative method as well as non-restarted methods such as BiCGSTAB. These methods offer an alternative to block methods, and they can also be combined with a block approach. An example is given showing significant improvement for a problem from quantum chromodynamics.

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BibTeXRIS

Ronald B. Morgan, Walter Wilcox. 2004-07-13. Deflated Iterative Methods for Linear Equations with Multiple Right-Hand Sides. https://arxiv.org/abs/math-ph/0405053

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