We investigate the NP-hard absolute value equation (AVE) Ax−|x|=b, where A is an arbitrary n×n real matrix. In this paper, we propose a smoothing Newton method for the AVE. When the singular values of A exceed 1, we show that this proposed method is globally convergent and the convergence rate is quadratic. Preliminary numerical results show that this method is promising.
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机译：我们研究NP硬绝对值方程（AVE）Ax- | x | = b，其中A是任意n×n实矩阵。在本文中，我们为AVE提出了一种平滑牛顿法。当A的奇异值超过1时，我们表明该方法是全局收敛的，收敛速度是二次的。初步数值结果表明该方法是有前途的。
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