Name
Title | ||
|---|---|---|
Constructing higher-order methods for obtaining the multiple roots of nonlinear equations |
Abstract | ||
|---|---|---|
This paper concentrates on iterative methods for obtaining the multiple roots of nonlinear equations. Using the computer algebra system Mathematica, we construct an iterative scheme and discuss the conditions to obtain fourth-order methods from it. All the presented fourth-order methods require one-function and two-derivative evaluation per iteration, and are optimal higher-order iterative methods for obtaining multiple roots. We present some special methods from the iterative scheme, including some known already. Numerical examples are also given to show their performance. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1016/j.cam.2011.03.014 | J. Computational Applied Mathematics |
Keywords | Field | DocType |
computer algebra system mathematica,two-derivative evaluation,special method,nonlinear equation,fourth-order method,iterative scheme,numerical example,multiple root,higher-order method,optimal higher-order iterative method,iterative method,nonlinear equations,iteration method,indexation,higher order | Mathematical optimization,Nonlinear system,Algebra,Iterative method,Mathematical analysis,Relaxation (iterative method),Symbolic computation,Local convergence,Mathematics | Journal |
Volume | Issue | ISSN |
235 | 14 | 0377-0427 |
Citations | PageRank | References |
29 | 1.23 | 7 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Xiaojian Zhou | 1 | 74 | 9.19 |
| Xin Chen | 2 | 151 | 22.93 |
| Yongzhong Song | 3 | 128 | 22.82 |