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IMA Journal of Numerical Analysis Advance Access originally published online on January 22, 2008
IMA Journal of Numerical Analysis 2008 28(3):598-618; doi:10.1093/imanum/drm039
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© The author 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Block preconditioning of real-valued iterative algorithms for complex linear systems

Michele Benzi{dagger}

Department of Mathematics and Computer Science, Emory University, Atlanta, GA 30322, USA

Daniele Bertaccini{ddagger}

Dipartimento di Matematica, Università di Roma "Tor Vergata", 00133 Roma, Italy

{dagger} Corresponding author. Email: benzi{at}mathcs.emory.edu

{ddagger} Email: bertaccini{at}mat.uniroma2.it

Received on 16 October 2006. Revised on 7 September 2007.


  Abstract

We revisit real-valued preconditioned iterative methods for the solution of complex linear systems, with an emphasis on symmetric (non-Hermitian) problems. Different choices of the real equivalent formulation are discussed, as well as different types of block preconditioners for Krylov subspace methods. We argue that if either the real or the symmetric part of the coefficient matrix is positive semidefinite, block preconditioners for real equivalent formulations may be a useful alternative to preconditioners for the original complex formulation. Numerical experiments illustrating the performance of the various approaches are presented.

Key Words: complex symmetric systems; Krylov subspace methods; block preconditioners; Schur complement; Helmholtz equation


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