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Simple geometric constructions of quadratically and cubically convergent iterative functions to solve nonlinear equations.
- Source :
-
Numerical Algorithms . Jan2008, Vol. 47 Issue 1, p95-107. 13p. - Publication Year :
- 2008
-
Abstract
- Abstract  In this paper, we derive one-parameter families of Newton, Halley, Chebyshev, Chebyshev-Halley type methods, super-Halley, C-methods, osculating circle and ellipse methods respectively for finding simple zeros of nonlinear equations, permitting f ′ (x) = 0 at some points in the vicinity of the required root. Halley, Chebyshev, super-Halley methods and, as an exceptional case, Newton method are seen as the special cases of the family. All the methods of the family and various others are cubically convergent to simple roots except Newton’s or a family of Newton’s method. [ABSTRACT FROM AUTHOR]
- Subjects :
- *EQUATIONS
*NONLINEAR theories
*MATHEMATICS
*MATHEMATICAL analysis
Subjects
Details
- Language :
- English
- ISSN :
- 10171398
- Volume :
- 47
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Numerical Algorithms
- Publication Type :
- Academic Journal
- Accession number :
- 28699288
- Full Text :
- https://doi.org/10.1007/s11075-007-9149-4