Optimization of the Hermitian and Skew-Hermitian Splitting Iteration for Saddle-Point Problems |
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Authors: | Michele Benzi Martin J. Gander Gene H. Golub |
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Abstract: | We study the asymptotic rate of convergence of the alternating Hermitian/skew-Hermitian iteration for solving saddle-point problems arising in the discretization of elliptic partial differential equations. By a careful analysis of the iterative scheme at the continuous level we determine optimal convergence parameters for the model problem of the Poisson equation written in div-grad form. We show that the optimized convergence rate for small mesh parameter h is asymptotically 1–O(h1/2). Furthermore we show that when the splitting is used as a preconditioner for a Krylov method, a different optimization leading to two clusters in the spectrum gives an optimal, h-independent, convergence rate. The theoretical analysis is supported by numerical experiments.This revised version was published online in October 2005 with corrections to the Cover Date. |
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Keywords: | HSS iteration saddle-point problems Fourier analysis rates of convergence |
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