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

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

2007-07-03

arxiv.org/abs/0707.0505v1

Physics

Mathematical Physics

13 pages, 5 figures

Scientific paper

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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