基于熵函数的梯度型算法求解绝对值方程  

The Conjugate Gradient Algorithm for Solving the Absolute Value Equations Based on Maximum Entropy Function

作　　者：祝文娟[1] 严涛[1] 

机构地区：[1]南京理工大学理学院,江苏南京210094

出　　处：《合肥师范学院学报》2016年第3期1-4,9,共5页Journal of Hefei Normal University

基　　金：国家自然科学基金项目(11101214)

摘　　要：本文中,在假设矩阵A的奇异值大于1的条件下,给出了求解绝对值方程的一个新的光滑化梯度型算法.通过引入极大熵函数对绝对值方程进行光滑化处理,得到一个非线性光滑方程组,再引入适当的目标函数,把绝对值方程转化为无约束优化问题,进而利用共轭梯度算法对其求解,从而获得原问题的解.数值实验表明了新方法的有效性.In this paper, a new smoothing conjugate gradient algorithm for solving absolute value equations is proposed under the condition that all singular values of matric A exceed one. By using the maximum entropy function, absolute value equation problems are transformed into a smooth nonlinear equations, and then into an unconstrained optimization problem by introducing appropriate objective function. We apply the conjugate gradient algorithm for solving the absolute value equation. Numerical results are presented to show efficiency of the new method.

关 键 词：绝对值方程 极大熵函数 共轭梯度法 无约束最优化 

分 类 号：O24[理学—计算数学]