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Convergence results for some piecewise linear solvers

Radons, Manuel; Rump, Siegfried M.

Let A be a real n×n matrix and z,b∈Rn. The piecewise linear equation system z−A|z|=b is called an absolute value equation. In this note we consider two solvers for uniquely solvable instances of the latter problem, one direct, one semi-iterative. We slightly extend the existing correctness, resp. convergence, results for the latter algorithms and provide numerical tests.
Published in: Optimization Letters, 10.1007/s11590-021-01837-7, Springer Nature