Abstract
A new algorithm is proposed for computing the intersection of two plane curves given in rational parametric form. It relies on the Ehrlich–Aberth iteration complemented with some computational tools like the properties of Sylvester and Bézout matrices, a stopping criterion based on the concept of pseudo-zero, an inclusion result and the choice of initial approximations based on the Newton polygon. The algorithm is implemented as a Fortran 95 module. From the numerical experiments performed with a wide set of test problems it shows a better robustness and stability with respect to the Manocha–Demmel approach based on eigenvalue computation. In fact, the algorithm provides better approximations in terms of the relative error and performs successfully in many critical cases where the eigenvalue computation fails.
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Bini, D.A., Marco, A. Computing curve intersection by means of simultaneous iterations. Numer Algor 43, 151–175 (2006). https://doi.org/10.1007/s11075-006-9048-0
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DOI: https://doi.org/10.1007/s11075-006-9048-0