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Name:
Miloslav Znojil
Reviewer number:
9689
Email:
znojil@ujf.cas.cz
Item's zbl-Number:
DE 017 526 609
Author(s):
Krukier, L. A.; Chikina, L. G.:
Shorttitle:
A two-cycle triangular-matrix iterative method for solving strongly asymmetric systems
Source:
Izv. Vyssh. Uchebn. Zaved., Mat. 2001, No. 5, 36 - 42 (2001).
Classification:
65N22Solution of discretized equations
Primary Classification:
65F10Iterative methods for linear systems
Secondary Classification:
76R10Free convection
Keywords:
convection-diffusion equation in two dimensions; five-point Runge Kutta method; predominantly skew-symmetric matrix; preconditioning using triangular matrices; iteration method with even and odd steps;
Review:


Non-homogeneous linear matrix equations with an almost skew-symmetric
matrix are considered. Their study is motivated by the needs of
hydrodynamics with predominant convection (and numerically
illustrated, via five-point Runge Kutta, by the convection-diffusion
equation in two dimensions). Their iterative treatment is based on an
older method proposed by one of the authors (L. A. K.). Its novelty
lies in the separation of even and odd iterations (= a special case
of the so called cyclic methods) which proved able to economize up to
40 percent of computing time in practice. Formulation of the explicit
convergence criteria and the estimates of the rate of convergence are
given, and an optimalization of the choice of free parameters is
discussed.
Remarks to the editors:

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