Method of Alternating Projection for the Absolute Value Equation
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A novel approach for solving the general absolute value equation Ax+B|x| = c where A,B∈ℝ^m× n and c∈ℝ^m is presented. We reformulate the equation as a 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 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≠ n, both theoretically and numerically.
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