LP narrowing: A new strategy for finding all solutions of nonlinear equations
LP narrowing: A new strategy for finding all solutions of nonlinear equations
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DOI：
10.1016/j.amc.2009.05.017
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发表时间：
2009-09
期刊：
影响因子：
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通讯作者：
K. Yamamura;Koki Suda;N. Tamura
中科院分区：
文献类型：
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作者：
K. Yamamura;Koki Suda;N. Tamura
本文提出了一种求n个非线性方程组全部解的有效算法。该算法是基于区间分析和一种新的策略称为LP缩小。在LP缩小策略中，不包含解的框（解域中的n维矩形）被排除，并且包含解的框被缩小，使得通过使用线性规划技术没有解丢失。由于LP窄化非常强大，因此可以非常有效地找到所有解决方案。数值算例表明，该算法能在实际计算时间内求出5000- 50000个非线性方程组的全部解。
An efficient algorithm is proposed for finding all solutions of systems of n nonlinear equations. This algorithm is based on interval analysis and a new strategy called LP narrowing. In the LP narrowing strategy, boxes (n-dimensional rectangles in the solution domain) containing no solution are excluded, and boxes containing solutions are narrowed so that no solution is lost by using linear programming techniques. Since the LP narrowing is very powerful, all solutions can be found very efficiently. By numerical examples, it is shown that the proposed algorithm could find all solutions of systems of 5000–50,000 nonlinear equations in practical computation time.