Solving polynomial systems (Q1098563)
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scientific article; zbMATH DE number 4039143
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Solving polynomial systems |
scientific article; zbMATH DE number 4039143 |
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Solving polynomial systems (English)
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1987
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The paper presents a short but very essential review of the main ideas on the homotopy continuation method of solving polynomial systems by means of reducing them to some Cauchy problem for a corresponding system of ordinary differential equations. Starting from a simple example the author discusses all the possible difficulties in the application of the method, especially so-called deficient polynomial systems. One of the more general results on the subject - the theorem on `random product homotopy' is formulated and its application to finding of equilibrium points of the four-dimensional Lorenz attractor is presented.
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homotopy continuation method
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polynomial systems
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Cauchy problem
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random product homotopy
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four-dimensional Lorenz attractor
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