From Fractal Behavior of Iteration Methods to an Efficient Solver for the Sign of a Matrix

Investigating the fractal behavior of iteration methods on special polynomials can help to find iterative methods with global convergence for finding special matrix functions. By employing such a methodology, we propose a new solver for the sign of an invertible square matrix. The presented method achieves the fourth rate of convergence by using as few matrix products as possible. Its attraction basin shows larger convergence radii, in contrast to its Pade-type methods of the same order. Computational tests are performed to check the efficacy of the proposed solver.