Abstract
We give a hybrid algorithm for solving non-linear polynomial systems. It is based on a branch-and-prune algorithm, combined with classical numerical methods, symbolic methods and interval methods. For some kinds of problems, Gather-and-Sift method, a symbolic method proposed by L. Yang, was used to reduce the dependency of variables or occurrences of the same variable, then interval methods were used to isolate the real roots. Besides these, there are some intelligent judgments which can improve the system’s efficiency significantly. The algorithm presented here works rather efficiently for some kinds of tests.
This research was partially supported by NSFC (10172028).
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Xue, J., Li, Y., Feng, Y., Yang, L., Liu, Z. (2004). An Intelligent Hybrid Algorithm for Solving Non-linear Polynomial Systems. In: Bubak, M., van Albada, G.D., Sloot, P.M.A., Dongarra, J. (eds) Computational Science - ICCS 2004. ICCS 2004. Lecture Notes in Computer Science, vol 3037. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24687-9_4
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