14:00
Polynomial preconditioning for linear solvers is well-known but not frequently used in current scientific applications. Furthermore, polynomial preconditioning has long been touted as well-suited for parallel computing; does this claim still hold in our new world of GPU-dominated machines? We give details of the GMRES polynomial preconditioner and discuss its simple implementation, its properties such as eigenvalue remapping, and choices such as the starting vector and added roots. We compare polynomial preconditioned GMRES to related methods such as FGMRES and full GMRES without restarting. We conclude with initial evaluations of the polynomial preconditioner for parallel and GPU computing, further discussing how polynomial preconditioning can become useful to real-word applications.
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