Numeric vs. symbolic homotopy algorithms in polynomial system solving: a case study (Q2387419)
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| Language | Label | Description | Also known as |
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| English | Numeric vs. symbolic homotopy algorithms in polynomial system solving: a case study |
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Numeric vs. symbolic homotopy algorithms in polynomial system solving: a case study (English)
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2 September 2005
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A family of systems of polynomial equations is considered, which arises in the analysis of the stationary solutions of certain discretized semi-linear parabolic differential equations. Only the positive solutions are of interest. A numerical homotopy algorithm for finding all positive solutions is presented with polynomial complexity in the number of unknown. It is shown that any universal symbolic method is likely to have a complexity which is exponential in the number of unknowns.
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polynomial systems
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homotopy methods
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symbolic methods
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complexity
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semi-linear parabolic problems
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positive solutions
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