A new family of eighth-order iterative methods for solving nonlinear equations

作者：Bi Weihong^*; Wu Qingbiao; Ren Hongmin

来源：Applied Mathematics and Computation, 2009, 214(1): 236-245.

DOI：10.1016/j.amc.2009.03.077

• Nonlinear equations
• Iterative methods
• Newton's method
• King's methods
• Order of convergence

A family of eighth-order iterative methods with four evaluations for the solution of nonlinear equations is presented. Kung and Traub conjectured that an iteration method without memory based on n evaluations could achieve optimal convergence order 2(n-1). The new family of eighth-order methods agrees with the conjecture of Kung-Traub for the case n = 4. Therefore this family of methods has efficiency index equal to 1.682. Numerical comparisons are made with several other existing methods to show the performance of the presented methods.

• 出版日期2009-8
• 单位浙江大学