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 with global convergence for finding matrix functions. By employing such a methodology, we propose new solver sign an invertible square matrix. The presented method achieves fourth rate by using as few products possible. Its attraction basin shows larger radii, in contrast its Padé-type same order. Computational tests are performed check efficacy proposed solver.