一类不可微方程组的区间算法

Interval algorithm for one class of non-differentiable equations

针对不可微方程组—绝对值方程Ax+B|x|=b的数值解问题进行研究,提出了通过构造极大熵函数和新的区间算子对方程进行求解的区间极大熵算法。该算法能同时求出绝对值方程的近似解和估算其近似解的误差限,并在A的奇异值全部大于|B|的奇异值时,证明了算法的收敛性且收敛速度至少是线性的。理论分析和数值结果均表明提出的算法是有效的。

This paper concerned with the non-differentiable equations and the absolute value equations. Based on maximum entropy and a new interval opeator, this paper proposed a interval maximum entropy algorithm which could solve the absolute value equations and estimate error between real solution and approximate solution. It proved the convergence and linear convergent rate when the singular values of A exceeded the singular value of ｜B｜. Theoretic analysis and numerical results show the method is effective.