A numerically stable high-order Chebyshev-Halley type multipoint iterative method for calculating matrix sign function

Abstract

A new eighth-order Chebyshev-Halley type iteration is proposed for solving nonlinear equations and matrix sign function. Basins of attraction show that several special cases of the new method are globally convergent. It is analytically proven that the new method is asymptotically stable and the new method has the order of convergence eight as well. The effectiveness of the theoretical results are illustrated by numerical experiments. In numerical experiments, the new method is applied to a random matrix, Wilson matrix and continuous-time algebraic Riccati equation. Numerical results show that, compared with some well-known methods, the new method achieves the accuracy requirement in the minimum computing time and the minimum number of iterations.

Keywords

• chebyshev-halley family
• iterative method
• basin of attraction
• matrix sign function
• stability