New algorithms to solve equations and systems in ordered spaces (Q2784161)
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scientific article; zbMATH DE number 1731165
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | New algorithms to solve equations and systems in ordered spaces |
scientific article; zbMATH DE number 1731165 |
Statements
8 January 2003
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partially ordered spaces
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nonliner operator equations
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systems
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fixed points
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algorithms
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numerical examples
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implicit equations
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New algorithms to solve equations and systems in ordered spaces (English)
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The author proves an existence theorem for the equation \(Lu=Nu\), where \(L\) and \(N\) are mappings to a partially ordered set and the range of \(N\) is a finite subset of the range of \(L\). The presented proof implies an algorithm for solving the equation. The basic results are applied to systems of equations, to systems of real functions, to implicit equations of the form \(Lu=Q(u,Lu)\) and to systems. Three concrete examples of the algorithm are also given.
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