Condition number based complexity estimate for solving polynomial systems |
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Authors: | Zhikun She Bican XiaZhiming Zheng |
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Affiliation: | a SKLSDE, LMIB and School of Mathematics and Systems Science, Beihang University, Beijing, Chinab School of Mathematical Sciences, Peking University, Beijing, China |
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Abstract: | By modifying and combining algorithms in symbolic and numerical computation, we propose a real-root-counting based method for deciding the feasibility of systems of polynomial equations. Along with this method, we also use a modified Newton operator to efficiently approximate the real solutions when the systems are feasible. The complexity of our method can be measured by a number of arithmetic operations which is singly exponential in the number of variables. |
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Keywords: | primary, 68W40 secondary, 68W30 |
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