A discrete maximum principle is presented for linear algebraic systems with coefficients of arbitrary signs and the number of unknowns exceeding (in the general case) the number of equations. The presentation uses the formal language of linear algebra (without any notions from the theory of difference schemes). This formal algebraic approach allows one to reveal easily the existence or absence of data for realization of an extended maximum principle in any algorithm represented in the form of a system of linear algebraic equations. The theorems formulated here directly imply the absolute stability of solutions to systems of equations. Variants of homogeneous algebraic systems and systems of equations with a right-hand side are considered. Theoretical results are illustrated by examples of actual problems.
Editor-in-Chief: Marchuk, Guri I.
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Extension of the algebraic aspect of the discrete maximum principle
1Institute of Numerical Mathematics and Mathematical Geophysics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk 630090, Russia
Citation Information: Russian Journal of Numerical Analysis and Mathematical Modelling rnam. Volume 22, Issue 6, Pages 601–614, ISSN (Online) 1569-3988, ISSN (Print) 0927-6467, DOI: 10.1515/rnam.2007.031, January 2008
- Published Online:
- 2008-01-27
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