A fast and efficient Newton-type iterative scheme to find the sign of a matrix

This work proposes a new scheme under the umbrella of iteration methods to compute the sign of an invertible matrix. To this target, a review of the exiting solvers of the same type is given and then a new scheme is derived based on a multi-step Newton-type nonlinear equation solver. It is shown that the new method and its reciprocal converge globally with wider convergence radii in contrast to their competitors of the same order from the general Padé schemes. After investigation on the theoretical parts, numerical experiments based on complex matrices of various sizes are furnished to reveal the superiority of the proposed solver in terms of elapsed CPU time.