A unified preconditioned minimal residual (PMR) algorithm for matrix problems: Linear systems, multiple right-hand sides linear systems, least squares problems, inversion and pseudo-inversion with application to color image encryption - Shirilord, Akbar; Dehghan, Mehdi (Applied numerical mathematics, 2026)
In this article, we introduce a preconditioned minimal residual (PMR) algorithm designed to address a wide range of matrix equations and linear systems. We illustrate the efficacy of this algorithm through several numerical examples, including the solution of matrix equations. Notably, we tackle various significant problems such as the minimization of Frobenius norms, least squares optimization, and the computation of the Moore-Penrose pseudo-inverse. Convergence analysis shows that it converges without any constraints and for any initial guess, although this algorithm is more efficient when the matrices are sparse. To validate the effectiveness of our proposed iterative algorithm, we offer various numerical examples by large matrices. As an application of the matrix equation, we explore a method for encrypting and decrypting color images.