ArticlesNo Access

ON JARRATT'S FAMILY OF OPTIMAL FOURTH-ORDER ITERATIVE METHODS AND THEIR DYNAMICS

Changbum Chun

Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Republic of Korea

Search for more papers by this author

Beny Neta

Naval Postgraduate School, Department of Applied Mathematics, Monterey, CA 93943, USA

Corresponding author.

Search for more papers by this author

, and

Sujin Kim

Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Republic of Korea

Search for more papers by this author

https://doi.org/10.1142/S0218348X14500133Cited by:27 (Source: Crossref)

Abstract

P. Jarratt has developed a family of fourth-order optimal methods. He suggested two members of the family. The dynamics of one of those was discussed previously. Here we show that the family can be written using a weight function and analyze all members of the family to find the best performer.

Keywords:

References

A. M. Ostrowski , Solution of Equations in Euclidean and Banach Space ( Academic Press , New York , 1973 ) . Google Scholar
J. F. Traub , Iterative Methods for the Solution of Equations ( Chelsea Publishing Company , New York , 1977 ) . Google Scholar
B. Neta , Numerical Methods for the Solution of Equations ( California , 1983 ) . Google Scholar
M. S. Petković et al. , Multipoint Methods for Solving Nonlinear Equations ( Elsevier , Waltham, MA , 2013 ) . Google Scholar
E. Halley , Philos. Trans. Roy. Soc. Lond. 18 , 136 ( 1694 ) . Crossref, Google Scholar
C. Chun et al. , Appl. Math. Comput. 218 , 6427 ( 2012 ) . Crossref, Web of Science, Google Scholar
P. Jarratt , Math. Comp. 20 , 434 ( 1966 ) . Crossref, Web of Science, Google Scholar
B. D. Stewart, Attractor basins of various root-finding methods, M.S. thesis, Naval Postgraduate School, Department of Applied Mathematics, Monterey, CA, June 2001 . Google Scholar
S. Amat, S. Busquier and S. Plaza, Iterative root-finding methods, unpublished report, 2004 . Google Scholar
S. Amat , S. Busquier and S. Plaza , Scientia 10 , 3 ( 2004 ) . Google Scholar
S. Amat , S. Busquier and S. Plaza , Appl. Math. Comput. 154 , 735 ( 2004 ) . Crossref, Web of Science, Google Scholar
S. Amat , S. Busquier and S. Plaza , Aeq. Math. 69 , 212 ( 2005 ) . Crossref, Google Scholar
M. Scott , B. Neta and C. Chun , Appl. Math. Comput. 218 , 2584 ( 2011 ) . Crossref, Web of Science, Google Scholar
F. Chircharro et al. , Appl. Math. Comput. 219 , 7023 ( 2013 ) . Crossref, Web of Science, Google Scholar
A. Cordero et al. , Appl. Math. Lett. 26 , 842 ( 2013 ) . Crossref, Web of Science, Google Scholar
B. Neta , M. Scott and C. Chun , Appl. Math. Comput. 218 , 10548 ( 2012 ) . Crossref, Web of Science, Google Scholar
B. Neta , M. Scott and C. Chun , Appl. Math. Comput. 218 , 5043 ( 2012 ) . Crossref, Web of Science, Google Scholar
B. Neta and C. Chun , Appl. Math. Comput. 219 , 10987 ( 2013 ) . Crossref, Web of Science, Google Scholar