Improving the efficiency of exclusion algorithms (Q2726409)
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scientific article; zbMATH DE number 1621023
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Improving the efficiency of exclusion algorithms |
scientific article; zbMATH DE number 1621023 |
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Improving the efficiency of exclusion algorithms (English)
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17 July 2001
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exclusion algorithm
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interval analysis
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homotopy method
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system of nonlinear equations
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numerical examples
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The author investigates exclusion algorithms as a tool in the area of interval analysis, for finding all solutions of a system of nonlinear equations. The homotopy and exclusion methods may be combined. Here an exclusion algorithm is used as a module to be investigated real components of a suitably reduced subproblem. One of the main results is a statement that summarizes the possible choices of exclusion tests, which are introduced here. It is shown as well that even degenerate zero points do not excessively increase the number of intervals generated by the algorithm, provided that a sufficiently tight test is used. A number of numerical examples is given to illustrate the statements.
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