Finding All Solutions of Nonlinear Equations Using the Dual Simplex Method (Self-validating numerical methods and related topics)
Finding All Solutions of Nonlinear Equations Using the Dual Simplex Method (Self-validating numerical methods and related topics)
复制标题
DOI：
10.1016/s0377-0427(02)00731-8
复制
发表时间：
2000-04
期刊：
影响因子：
--
通讯作者：
K. Yamamura;Shigeru Tanaka
中科院分区：
文献类型：
--
作者：
K. Yamamura;Shigeru Tanaka
最近，已经提出了一种有效的算法，用于使用线性规划来寻找非线性方程组的所有解。该算法基于使用对偶单纯形法对非线性方程组解不存在的简单测试（称为LP测试）。在这封信中，提出了一个改进的版本的LP测试算法。数值算例表明，该算法能在实际计算时间内求出300个非线性方程组的所有解。
Recently, an efficient algorithm has been proposed for finding all solutions of systems of nonlinear equations using linear programming. This algorithm is based on a simple test (termed the LP test) for nonexistence of a solution to a system of nonlinear equations using the dual simplex method. In this letter, an improved version of the LP test algorithm is proposed. By numerical examples, it is shown that the proposed algorithm could find all solutions of a system of 300 nonlinear equations in practical computation time.