A generalized Newton method for absolute value equations
A generalized Newton method for absolute value equations
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DOI：
10.1007/s11590-008-0094-5
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发表时间：
2009-01-01
影响因子：
1.6
通讯作者：
Mangasarian, O. L.
中科院分区：
文献类型：
--
作者：
Mangasarian, O. L.
提出了一种求解NP难绝对值方程Ax -垂直杆x垂直杆= B当A的奇异值大于1时的直接广义牛顿法。该方法的一个简单的MATLAB实现解决了100个随机生成的1,000维AVE，每个AVE的精度为10（-6），不到10 s。类似地，对应于100个随机生成的线性互补问题的AVE（具有1，000 x 1，000个非对称正定矩阵）也在不到29秒的时间内以相同的精度求解。
A direct generalized Newton method is proposed for solving the NP-hard absolute value equation (AVE) Ax -vertical bar x vertical bar = b when the singular values of A exceed 1. A simple MATLAB implementation of the method solved 100 randomly generated 1,000-dimensional AVEs to an accuracy of 10(-6) in less than 10 s each. Similarly, AVEs corresponding to 100 randomly generated linear complementarity problems with 1,000 x 1,000 nonsymmetric positive definite matrices were also solved to the same accuracy in less than 29 s each.