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Zh. Vychisl. Mat. Mat. Fiz., 2006, Volume 46, Number 6, Pages 963–974 (Mi zvmmf451)  

On the SOR method with overlapping subsystems

A. A. Maleev

Research Institute of Technical Physics, Box 245, Snezhinsk, 456770, Russia

Abstract: A description is given of the iterative Jacobi method with overlapping subsystems and the corresponding Gauss–Seidel method. Similarly to the classical case, a generalized SOR method with overlapping subsystems is constructed by introducing an relaxation parameter. The concept of a $\omega$-consistent matrix is defined. It is shown that, with the optimal choice of the parameter, the theory developed by Young remains valid for $\omega$-consistent matrices. This implies certain results for $\omega$-consistent $H$-matrices. The theoretical conclusions obtained in the paper are supported by numerical results.

Key words: iterative methods for SLAE, generalized SOR method, $H$-matrices.

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English version:
Computational Mathematics and Mathematical Physics, 2006, 46:6, 919–929

Bibliographic databases:

UDC: 519.612
Received: 09.09.2005

Citation: A. A. Maleev, “On the SOR method with overlapping subsystems”, Zh. Vychisl. Mat. Mat. Fiz., 46:6 (2006), 963–974; Comput. Math. Math. Phys., 46:6 (2006), 919–929

Citation in format AMSBIB
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\by A.~A.~Maleev
\paper On the SOR method with overlapping subsystems
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2006
\vol 46
\issue 6
\pages 963--974
\mathnet{http://mi.mathnet.ru/zvmmf451}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2285357}
\transl
\jour Comput. Math. Math. Phys.
\yr 2006
\vol 46
\issue 6
\pages 919--929
\crossref{https://doi.org/10.1134/S0965542506060017}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33746127557}


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