A cubic-order variant of Newton's method for finding multiple roots of nonlinear equations

作者：Kim Young Ik; Geum Young Hee^*

来源：Computers & Mathematics with Applications, 2011, 62(4): 1634-1640.

DOI：10.1016/j.camwa.2011.04.069

• Multiple root
• Order of convergence
• Newton's method
• Nonlinear equation
• Root finding

A second-derivative-free iteration method is proposed below for finding a root of a nonlinear equation f (x) = 0 with integer multiplicity m >= 1:
x(n+1) = x(n) - f(x(n) - mu f(x(n))/f'(x(n))) + gamma f(x(n))/f'(x(n)), n = 0, 1, 2, ....
We obtain the cubic order of convergence and the corresponding asymptotic error constant in terms of multiplicity m, and parameters mu and gamma. Various numerical examples are presented to confirm the validity of the proposed scheme.

• 出版日期2011-8