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BIT Numerical Mathematics

, Volume 43, Issue 5, pp 881–900 | Cite as

Optimization of the Hermitian and Skew-Hermitian Splitting Iteration for Saddle-Point Problems

  • Michele Benzi
  • Martin J. Gander
  • Gene H. Golub
Article

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.

HSS iteration saddle-point problems Fourier analysis rates of convergence 

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Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Michele Benzi
  • Martin J. Gander
  • Gene H. Golub

There are no affiliations available

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