New Polynomial Preconditioned GMRES
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A new polynomial preconditioner is given for solving large systems of linear equations. The polynomial is derived from the minimum residual polynomial and is straightforward to compute and implement. It this paper, we study the polynomial preconditioner applied to GMRES, however it could be used with any Krylov solver. This preconditioning algorithm can dramatically improve convergence for difficult problems and can reduce dot products by an even greater margin. Stability control using added roots allows for high degree polynomials, and we give an additional check for stability. This approach is compared to existing methods such as BiCGStab and FGMRES.
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