Toward efficient polynomial preconditioning for GMRES

We present a polynomial preconditioner for solving large systems of linear equations. The is derived from the minimum residual (the GMRES polynomial) and more straightforward to compute implement than many previous preconditioners. Our current implementation this using its roots naturally stable methods computing same polynomial. further stability control added roots, allows high degree polynomials. discuss effectiveness challenges root-adding give an additional check stability. In paper, we study applied GMRES; however it could be used with any Krylov solver. This preconditioning algorithm can dramatically improve convergence some problems, especially difficult reduce dot products by even greater margin.