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The fixed point iteration (FPI) method proposed by Ke [Appl Math Lett. 2020;99:105990] for solving the absolute value equations (AVE) with the formis interesting for its simplicity and efficiency. However, its convergence is only guaranteed for the case that, excluding the possible case that. To complete the gap, we develop a modified FPI (MFPI) method for solving the AVE with, which, besides keeping the simplicity of FPI, improves its efficiency by judiciously choosing the involving parameter. Under mild conditions, we prove its linear convergence. We present some preliminary numerical results for, demonstrating its convergence; and compare it with FPI when, illustrating its superiority.

A modified fixed point iteration method for solving the system of absolute value equations