Bekker, H.

Braad, E.P.

Goldengorin, B.

English

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

ARTS repository - University of Groningen

Using bipartite and multidimensional matching to select the roots of a system of polynomial equations

https://pure.rug.nl/ws/files/2895832/2005LNCSBekker1.pdf

Using bipartite and multidimensional matching to select the roots of a system of polynomial equations

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ARTS repository - University of Groningen