A globally convergent numerical method with fourth order for computing the matrix sign

Abstract

The target of this article is to propose a novel numerical scheme that can compete its corresponding solvers of the same type for computing the sign matrix. To do this, a three‐step root solver is designed to gain as much as possible of global convergence when finding the matrix sign. It is proved that the novel numerical scheme is of quartical convergence order. The stability of the scheme is discussed in detail as well. Finally, numerical tests are provided to uphold the theoretical findings.