Name
Abstract | ||
|---|---|---|
This paper presents two families of higher-order iterative methods for solving multiple roots of nonlinear equations. One is of order three and the other is of order four. The presented iterative families all require two evaluations of the function and one evaluation of its first derivative, thus the latter is of optimal order. The third-order family contains several iterative methods known already. And, different from the optimal fourth-order methods for multiple roots known already, the presented fourth-order family use the modified Newton's method as its first step. Local convergence analyses and some special cases of the presented families are given. We also carry out some numerical examples to show their performance. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1016/j.amc.2012.12.041 | Applied Mathematics and Computation |
Keywords | Field | DocType |
optimal fourth-order method,fourth-order family,nonlinear equation,optimal order,local convergence analysis,iterative family,higher-order iterative method,modified newton,multiple root,third-order family,iterative method,nonlinear equations | Mathematical optimization,Nonlinear system,Iterative method,Fourth order,Mathematical analysis,Derivative,Local convergence,Mathematics | Journal |
Volume | Issue | ISSN |
219 | 11 | 0096-3003 |
Citations | PageRank | References |
5 | 0.46 | 14 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Xiaojian Zhou | 1 | 74 | 9.19 |
| Xin Chen | 2 | 5 | 0.46 |
| Yongzhong Song | 3 | 128 | 22.82 |