Globally convergent iterative scheme for computing matrix sign function with numerical stability

Abstract

In this article, we have proposed a novel matrix iteration for computing the matrix sign function numerically. An extensive convergence analysis is carried out in matrix case to achieve fourth‐order convergence. The basins of attraction are drawn to illustrate the global convergence behavior of the proposed method. Analytically, it is shown that the presented scheme is asymptotically stable. Further, the theoretical developments are verified numerically by discussing eigenvalues clustering around . Moreover, a class of numerical examples for matrices of various dimensions is assessed to exhibit the efficacy of proposed method.