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

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Abstract

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.

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Authors and Affiliations

  1. King Abdulaziz University, Jeddah, Saudi Arabia

    Owe Axelsson & Bashir Ahmad

  2. Institute of Geonics, AVSR, Ostrava, Czech Republic

    Owe Axelsson

  3. Department of Information Technology, Uppsala University, Uppsala, Sweden

    Maya Neytcheva

Authors
  1. Owe Axelsson
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  2. Maya Neytcheva
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  3. Bashir Ahmad
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Correspondence to Maya Neytcheva.

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Axelsson, O., Neytcheva, M. & Ahmad, B. A comparison of iterative methods to solve complex valued linear algebraic systems. Numer Algor 66, 811–841 (2014). https://doi.org/10.1007/s11075-013-9764-1

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