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

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.