Two new classes of optimal Jarratt-type fourth-order methods

Applied Mathematics Letters

Volumn 25, Issue 5, 2012, Pages 847-853

  Soleymani, F ^a   Khattri, S K ^b   Karimi Vanani, S ^a  

^a ISLAMIC AZAD UNIVERSITY   (Iran)

^b WESTERN NORWAY UNIVERSITY OF APPLIED SCIENCES   (Norway)

Author keywords

Efficiency index; Jarratt type methods; KungTraub conjecture; Multi point iterations; Optimal order

Indexed keywords

EFFICIENCY INDEX; JARRATT-TYPE METHODS; KUNGTRAUB CONJECTURE; MULTI-POINT ITERATIONS; OPTIMAL ORDER;

OPTIMIZATION;

NONLINEAR EQUATIONS;

EID: 84856368465     PISSN: 08939659     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.aml.2011.10.030     Document Type: Article

References (13)

1. S.K. Khattri Optimal eighth order iterative methods Math. Comput. Sci. 2011 10.1007/s11786-011-0064-7
2. P. Sargolzaei, and F. Soleymani Accurate fourteenth-order methods for solving nonlinear equations Numer. Algorithms 2011 10.1007/s11075-011-9467-4
3. F. Soleymani, M. Sharifi, and B.S. Mousavi An improvement of Ostrowski's and King's techniques with optimal convergence order eight J. Optim. Theory Appl. 2011 10.1007/s10957-011-9929-9
4. C. Chun, and B. Neta Certain improvements of Newton's method with fourth-order convergence Appl. Math. Comput. 215 2009 821 828
5. S. Weerakoon, and G.I. Fernando A variant of Newton's method with accelerated third-order convergence Appl. Math. Lett. 17 2000 87 93
6. M. Frontini, and E. Sormani Some variants of Newton's method with third-order convergence Appl. Math. Comput. 140 2003 419 426
7. H.H.H. Homeier On Newton-type methods with cubic convergence J. Comput. Appl. Math. 176 2005 425 432 (Pubitemid 40060261)
8. P. Jarratt Some efficient fourth order multipoint methods for solving equations BIT 9 1969 119 124
9. S.K. Khattri, and S. Abbasbandy Optimal fourth order family of iterative methods Mat. Vesnik 63 2011 67 72
10. H.T. Kung, and J.F. Traub Optimal order of one-point and multipoint iteration J. Assoc. Comput. Mach. 21 1974 634 651
11. F. Soleymani, S. Karimi Vanani, M. Khan, and M. Sharifi Some modifications of King's family with optimal eighth order of convergence Math. Comput. Modelling 2011 10.1016/j.mcm.2011.10.016
12. F. Soleymani, and S. Karimi Vanani Optimal Steffensen-type methods with eighth order of convergence Comput. Math. Appl. 2011 10.1016/j.camwa.2011.10.047
13. F. Soleymani A novel and precise sixth-order method for solving nonlinear equations Int. J. Math. Models Methods Appl. Sci. 5 2011 730 737