A simple modification of Newton%26apos;s method to achieve convergence of order 1+root 2

作者：McDougall Trevor J^*; Wotherspoon Simon J

来源：Applied Mathematics Letters, 2014, 29: 20-25.

DOI：10.1016/j.aml.2013.10.008

• Newton%26apos
• s method
• Non-linear equations
• Root-finding
• Iterative methods

A simple modification to the standard Newton method for approximating the root of a univariate function is described and analyzed. For the same number of function and derivative evaluations, the modified method converges faster, with the convergence order of the method being 1 + root 2 approximate to 2.4 compared with 2 for the standard Newton method. Numerical examples demonstrate the faster convergence achieved with this modification of Newton%26apos;s method. This modified Newton-Raphson method is relatively simple and is robust; it is more likely to converge to a solution than are either the higher order (4th order and 6th order) schemes or Newton%26apos;s method itself.

• 出版日期2014-3