A two-steps fixed-point method for solving a general absolute value matrix equation

Abstract

This dissertation investigates a class of General Absolute Value Matrix Equations (GAVME) of the form: AX−B|X| = C, (A, B, C ∈ ℝ𝑛?×𝑛?,) are given matrices. We derive several weakened sufficient conditions to guarantee the unique solvability of the GAVME. For its numerical solution, a two-steps Picard’s and fixed-point iterative methods are proposed. Furthermore, we establish that under suitable assumptions, the proposed algorithms are well- defined and exhibit global linear convergence toward the unique solution of the GAVME. To conclude, a diverse array of numerical experiments is presented to substantiate the efficiency and robustness of our approach