A novel approach for solving the general absolute value equation \(Ax+B|x| = c\) where \(A,B\in \textrm{I}\! \textrm{R}^{m\times n}\) and \(c\in \textrm{I}\! \textrm{R}^m\) is presented. We reformulate the equation as a nonconvex feasibility problem which we solve via the method of alternating projections (MAP). The fixed points set of the alternating projections map is characterized under nondegeneracy conditions on A and B. Furthermore, we prove local linear convergence of the algorithm. Unlike most of the existing approaches in the literature, the algorithm presented here is capable of handling problems with \(m\ne n\), both theoretically and numerically.

一种求解一般绝对值方程\(Ax+B|x| = c\)的新方法，其中\(A,B\in \textrm{I}\! \textrm{R}^{m\times n}\ )和\(c\in \textrm{I}\! \textrm{R}^m\)被呈现。我们将方程重新表述为一个非凸可行性问题，我们通过交替投影 (MAP) 方法解决该问题。交替投影映射的固定点集在A和B上的非退化条件下进行表征。此外，我们证明了算法的局部线性收敛性。与文献中的大多数现有方法不同，这里提出的算法能够在理论上和数值上处理\(m\ne n\)的问题。