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- W2015872029 abstract "Considered are two kinds of monotonicity properties of systems of linear equations. Firstly, a maximum principle is defined for matrices of monotone kind, and sufficient conditions are given for its validity. Secondly, for more special systems, sufficient conditions are established under which (componentwise) monotonicity of the right-hand side implies monotonicity of the solution. A series of examples is considered for the investigated concepts, mainly from the context of difference schemes, leading to some new results for well-known schemes. Es werden zwei Arten von Monotonie-Eigenschaften linearer Gleichungssysteme betrachtet: Für Matrizen monotoner Art werden ein Maximumprinzip definiert und hinreichende Bedingungen für seine Gültigkeit angegeben. Für speziellere Gleichungssysteme werden Bedingungen hergeleitet, unter denen die (komponentenweise) Monotonie der rechten Seite die Monotonic der Lösung nach sich zieht. Für die untersuchten Begriffe wird eine Reihe von Beispielen betrachtet, wobei die Anwendung auf bekannte Differenzenverfahren zu einigen neuen Ergebnissen führt." @default.
- W2015872029 created "2016-06-24" @default.
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- W2015872029 date "1982-01-01" @default.
- W2015872029 modified "2023-09-26" @default.
- W2015872029 title "On a Maximum Principle for Matrices, and on Conservation of Monotonicity. With Applications to Discretization Methods" @default.
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- W2015872029 doi "https://doi.org/10.1002/zamm.19820620804" @default.
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