Abstract
ABSTRACT The fixed point iteration (FPI) method proposed by Ke [Appl Math Lett. 2020;99:105990] for solving the absolute value equations (AVE) with the form is 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.
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