Numerical Algorithms

, Volume 66, Issue 4, pp 811–841 | Cite as

A comparison of iterative methods to solve complex valued linear algebraic systems

  • Owe Axelsson
  • Maya Neytcheva
  • Bashir Ahmad
Original Paper


Complex valued linear algebraic systems arise in many important applications. We present analytical and extensive numerical comparisons of some available numerical solution methods. It is advocated, in particular for large scale ill-conditioned problems, to rewrite the complex-valued system in real valued form leading to a two-by-two block system of particular form, for which it is shown that a very efficient and robust preconditioned iterative solution method can be constructed. Alternatively, in many cases it turns out that a simple preconditioner in the form of the sum of the real and the imaginary part of the matrix also works well but involves complex arithmetic.


Linear systems Complex symmetric Real valued form Preconditioning 


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.King Abdulaziz UniversityJeddahSaudi Arabia
  2. 2.Institute of Geonics, AVSROstravaCzech Republic
  3. 3.Department of Information TechnologyUppsala UniversityUppsalaSweden

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