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Name:  
Miloslav Znojil  
Reviewer number:  
9689  
Email:  
znojil@ujf.cas.cz  
Item's zblNumber:  
DE 017 526 609  
Author(s):  
Krukier, L. A.; Chikina, L. G.:  
Shorttitle:  
A twocycle triangularmatrix iterative method for solving strongly asymmetric systems  
Source:  
Izv. Vyssh. Uchebn. Zaved., Mat. 2001, No. 5, 36  42 (2001).  
Classification:  
 
Primary Classification:  
 
Secondary Classification:  
 
Keywords:  
convectiondiffusion equation in two dimensions; fivepoint Runge Kutta method; predominantly skewsymmetric matrix; preconditioning using triangular matrices; iteration method with even and odd steps;  
Review:  
Nonhomogeneous linear matrix equations with an almost skewsymmetric matrix are considered. Their study is motivated by the needs of hydrodynamics with predominant convection (and numerically illustrated, via fivepoint Runge Kutta, by the convectiondiffusion 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:  