Local and Semilocal Convergence of Wang-Zheng’s Method for Simultaneous Finding Polynomial Zeros

Abstract

In 1984, Wang and Zheng (J. Comput. Math. 1984, 1, 70−76) introduced a new fourth order iterative method for the simultaneous computation of all zeros of a polynomial. In this paper, we present new local and semilocal convergence theorems with error estimates for Wang−Zheng’s method. Our results improve the earlier ones due to Wang and Wu (Computing 1987, 38, 75−87) and Petković, Petković, and Rančić (J. Comput. Appl. Math. 2007, 205, 32−52).

Keywords

• iteration methods
• simultaneous methods
• polynomial zeros
• Wang–Zheng method
• local convergence
• semilocal convergence
• error estimates