Polynomial Preconditioned GMRES in Trilinos: Practical Considerations for High-Performance Computing

Polynomial preconditioners for GMRES and other Krylov solvers are well-known but are infrequently used in largescale software libraries or applications. This may be due to stability problems or complicated algorithms. We implement the GMRES polynomial as a preconditioner in the software library Trilinos and demonstrate that it is stable and effective for parallel computing. Trade-offs when selecting a polynomial degree and combining with other preconditioners are analyzed. We also discuss communication-avoiding (CA) properties of the polynomial and relate these to current

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