Name
Title | ||
|---|---|---|
Iterative methods based on the signum function approach for solving nonlinear equations |
Abstract | ||
|---|---|---|
For finding a root of an equation f(x) = 0 on an interval (a, b), we develop an iterative method using the signum function and the trapezoidal rule for numerical integrations based on the
recent work (Yun, Appl Math Comput 198:691–699, 2008). This method, so-called signum iteration method, depends only on the signum function independently of the behavior of f(x), and the error bound of the kth approximation is (b − a)/(2N
k
), where N is the number of integration points for the trapezoidal rule in each iteration. In addition we suggest hybrid methods which
combine the signum iteration method with usual methods such as Newton, Ostrowski and secant methods. In particular the hybrid
method combined with the signum iteration and the secant method is a predictor-corrector type method (Noor and Ahmad, Appl
Math Comput 180:167–172, 2006). The proposed methods result in the rapidly convergent approximations, without worry about choosing a proper initial guess.
By some numerical examples we show the superiority of the presented methods over the existing iterative methods. |
Year | DOI | Venue |
|---|---|---|
2009 | 10.1007/s11075-009-9305-0 | Numerical Algorithms |
Keywords | Field | DocType |
Signum function,Trapezoidal rule,Newton method,Secant method,65H05,68W25 | Mathematical optimization,Nonlinear system,Mathematical analysis,Iterative method,Trapezoidal rule,Mathematics,Secant method,Newton's method | Journal |
Volume | Issue | ISSN |
52 | 4 | 1017-1398 |
Citations | PageRank | References |
11 | 0.98 | 8 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Beong In Yun | 1 | 86 | 12.55 |
| Miodrag S. Petkovic | 2 | 104 | 15.28 |