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- W1750369710 abstract "Assume that the system of two polynomial equations f(x,y) = 0 and g(x,y) = 0 has a finite number of solutions. Then the solution consists of pairs of an x-value and an y-value. In some cases conventional methods to calculate these solutions give incorrect results and are complicated to implement due to possible degeneracies and multiple roots in intermediate results. We propose and test a two-step method to avoid these complications. First all x-roots and all y-roots are calculated independently. Taking the multiplicity of the roots into account, the number of x-roots equals the number of y-roots. In the second step the x-roots and y-roots are matched by constructing a weighted bipartite graph, where the x-roots and the y-roots are the nodes of the graph, and the errors are the weights. Of this graph the minimum weight perfect matching is computed. By using a multidimensional matching method this principle may be generalized to more than two equations." @default.
- W1750369710 created "2016-06-24" @default.
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- W1750369710 date "2005-01-01" @default.
- W1750369710 modified "2023-10-17" @default.
- W1750369710 title "Using Bipartite and Multidimensional Matching to Select the Roots of a System of Polynomial Equations" @default.
- W1750369710 cites W1535005156 @default.
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- W1750369710 doi "https://doi.org/10.1007/11424925_43" @default.
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