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A new approach is discussed for solving large nonsymmetric systems of linearequations with multiple right-hand sides. The first system is solved with adeflated GMRES method that generates eigenvector information at the same timethat the linear equations are solved. Subsequent systems are solved bycombining restarted GMRES with a projection over the previously determinedeigenvectors. This approach offers an alternative to block methods, and it canalso be combined with a block method. It is useful when there are a limitednumber of small eigenvalues that slow the convergence. An example is givenshowing significant improvement for a problem from quantum chromodynamics. Thesecond and subsequent right-hand sides are solved much quicker than without thedeflation. This new approach is relatively simple to implement and is veryefficient compared to other deflation methods.

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