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Mathematical Problems in Engineering - Volume 2015 2015, Article ID 548609, 20 pages -

Research ArticleDepartment of Industrial Engineering, University of Trento, Via Sommarive 9, Povo, 38123 Trento, Italy

Received 11 July 2014; Revised 4 November 2014; Accepted 27 November 2014

Academic Editor: Luca Bergamaschi

Copyright © 2015 Enrico Bertolazzi and Marco Frego. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A new preconditioner for symmetric complex linear systems based on Hermitian and skew-Hermitian splitting HSS for complex symmetric linear systems is herein presented. It applies to conjugate orthogonal conjugate gradient COCG or conjugate orthogonal conjugate residual COCR iterative solvers and does not require any estimation of the spectrum of the coefficient matrix. An upper bound of the condition number of the preconditioned linear system is provided. To reduce the computational cost the preconditioner is approximated with an inexact variant based on incomplete Cholesky decomposition or on orthogonal polynomials. Numerical results show that the present preconditioner and its inexact variant are efficient and robust solvers for this class of linear systems. A stability analysis of the inexact polynomial version completes the description of the preconditioner.

Author: Enrico Bertolazzi and Marco Frego



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