关键词: 绝对值方程, 极大熵函数, 牛顿迭代法

Abstract:

Absolute value equations(AVE) Ax-|x|=b,A∈R^n×n,b∈Rⁿ is a special class of nonlinear equations and it is NP-Hard.It is proved that absolute value equations can be transformed into a smoothing nonlinear equation by introducing the maximum entropy function.A Newton method is given to solve the smoothing nonlinear equations and its convergence is discussed.Numerical results show that this method is feasible and effective.

Key words: absolute value equation;maximum entropy function;Newton method