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

0397052 - ÚGN 2015 RIV NL eng J - Journal Article
Axelsson, Owe - Neytcheva, M. - Ahmad, B.
A comparison of iterative methods to solve complex valued linear algebraic systems.
Numerical Algorithms. Roč. 66, č. 4 (2013), s. 811-841. ISSN 1017-1398. E-ISSN 1572-9265
R&D Projects: GA MŠMT ED1.1.00/02.0070
Institutional support: RVO:68145535
Keywords : linear systems * complex symmetric * real valued form * preconditioning
Subject RIV: BA - General Mathematics
Impact factor: 1.005, year: 2013
http://www.it.uu.se/research/publications/reports/2013-005/2013-005-nc.pdf

Complex valued linear algebraic systems arise in many important applica- tions. 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.
Permanent Link: http://hdl.handle.net/11104/0224731