Polynomial Preconditioned Arnoldi
This work addresses the need for more efficient eigenvalue computation in scientific computing, particularly benefiting parallel computations by reducing communication-intensive operations.
Polynomial preconditioning improves the convergence of the Arnoldi method for eigenvalue computation, reducing orthogonalization costs and, for difficult problems, the number of matrix-vector products. A two-level double polynomial preconditioning strategy effectively generates high-degree preconditioners.
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.