Basin attractors for various methods

Applied Mathematics and Computation - Tập 218 Số 6 - Trang 2584-2599 - 2011
Melvin R. Scott1, Beny Neta2, Changbum Chun3
1494 Carlton Court, Ocean Isle Beach, NC 28469, USA
2Naval Postgraduate School, Department of Applied Mathematics, Monterey, CA 93943, USA#TAB#
3Department of Mathematics, Sungkyunkwan University, Suwon 440–746, Republic of Korea

Tóm tắt

Từ khóa


Tài liệu tham khảo

S. Amat, S. Busquier, S. Plaza, Iterative root-finding methods, unpublished report, 2004.

C. Chun, B. Neta, A New Sixth-Order Scheme for Nonlinear Equations, Appl. Math. Lett. accepted for publication.

Conte, 1973

Halley, 1694, A new, exact and easy method of finding the roots of equations generally and that without any previous reduction, Phil. Trans. Roy. Soc. London, 18, 136, 10.1098/rstl.1694.0029

Popovski, 1980, A family of one point iteration formulae for finding roots, Int. J. Comput. Math., 8, 85, 10.1080/00207168008803193

Laguerre, 1880, Sur une méthode pour obtener par approximation les racines d’une équation algébrique qui a toutes ses racines réelles, Nouvelles Ann. de Math. 2e séries, 19, 88

King, 1973, A family of fourth order methods for nonlinear equations, SIAM J. Numer. Amal., 10, 876, 10.1137/0710072

Kung, 1974, Optimal order of one-point and multipoint iterations, J. Assoc. Comput. Mach., 21, 643, 10.1145/321850.321860

Milnor, 2006

Murakami, 1978, Some fifth order multipoint iterative formulae for solving equations, J. Inform. Process., 1, 138

Neta, 1979, A sixth order family of methods for nonlinear equations, Int. J. Comput. Math., 7, 157, 10.1080/00207167908803166

Neta, 2008, High order nonlinear solver, J. Comput. Methods Sci. Eng., 8, 245

Jarratt, 1966, Multipoint iterative methods for solving certain equations, Comput. J., 8, 398, 10.1093/comjnl/8.4.398

Neta, 2010, Construction of optimal order nonlinear solvers using inverse interpolation, Appl. Math. Comput., 217, 2448, 10.1016/j.amc.2010.07.045

Neta, 1981, On a family of multipoint methods for nonlinear equations, Int. J. Comput. Math., 9, 353, 10.1080/00207168108803257

Ostrowski, 1973

B.D. Stewart, Attractor Basins of Various Root-Finding Methods, M.S. thesis, Naval Postgraduate School, Department of Applied Mathematics, Monterey, CA, June 2001.