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. © Springer-Verlag Berlin Heidelberg 2005.
CITATION STYLE
Bekker, H., Braad, E. P., & Goldengorin, B. (2005). Using bipartite and multidimensional matching to select the roots of a system of polynomial equations. In Lecture Notes in Computer Science (Vol. 3483, pp. 397–406). Springer Verlag. https://doi.org/10.1007/11424925_43
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