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论文类型：期刊论文

发表时间：2008-01-01

发表刊物：SIAM JOURNAL ON NUMERICAL ANALYSIS

收录刊物：SCIE、EI、Scopus

卷号：46

期号：3

页面范围：1503-1518

ISSN号：0036-1429

关键字：homotopy method; polynomial system; mixed trigonometric polynomial system; symbolic-numeric computation

摘要：Mixed trigonometric polynomial systems arise in many fields of science and engineering. Commonly, this class of systems is transformed into polynomial systems by variable substituting and adding some quadratic equations, and then solved by some polynomial system solving method. In this paper, by exploiting the special structure of the additional quadratic equations, an efficient hybrid method for solving polynomial systems coming from mixed trigonometric polynomial systems is presented. It combines the homotopy method, in which the homotopy is a combination of coefficient parameter homotopy and the random product homotopy, with decomposition, variable substitution, and reduction techniques. Numerical tests are given to show its effectiveness, and it is applied to solve a practical problem.