Polynomial preconditioning in Krylov-ROW-methods Original Research Article

Krylov methods, which may be used for solving the stage equations in ROW-methods, become increasingly expensive if large subspace dimensions are necessary. We show, that it is possible to switch adaptively to a polynomially preconditioned Krylov process if this situation occurs. We present an algorithm for condensation of the basis of the original Krylov subspace to the smaller basis of the preconditioned subspace. Numerical experiments confirm savings in time and memory requirements for small polynomial degree.