Polynomial preconditioning can improve the convergence of the Arnoldi method for computing eigenvalues. Such preconditioning significantly reduces the cost of orthogonalization; for difficult problems, it can also reduce the number of matrix-vector products. Parallel computations can particularly benefit from the reduction of communication-intensive operations. The GMRES algorithm provides a simple and effective way of generating the preconditioning polynomial. For some problems high degree polynomials are especially effective, but they can lead to stability problems that must be mitigated. A two-level “double polynomial preconditioning” strategy provides an effective way to generate high-degree preconditioners.
- Date of publication:
- SIAM Journal on Scientific Computing
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- Publication note:
Mark Embree, Jennifer A. Loe, Ronald B. Morgan: Polynomial Preconditioned Arnoldi with Stability Control. SIAM J. Sci. Comput. 43(1): A1-A25 (2021)