A polynomial preconditioner for the GMRES algorithm

The major drawback of GMRES is that the storage demands and the number of operations per iteration increase with the number of iterations. It is important to avoid that so many iterations are needed that the work per iteration and the storage requirements become unacceptably high. This paper describes a polynomial preconditioner with which this can be achieved efficiently. The polynomial preconditioner is constructed so that it has a minimization property in an area of the complex plane. A suitable area, and hence the preconditioning polynomial, can be obtained from eigenvalue estimates. The polynomial preconditioner is very simple and easy to implement.