A penta-parametric family of fifteenth-order multipoint methods for nonlinear equations

Applied Mathematics and Computation

Volumn 217, Issue 6, 2010, Pages 2311-2319

  Geum, Young Hee ^a   Kim, Young Ik ^a  

^a Dankook University   (South Korea)

Author keywords

Asymptotic error constant; Efficiency index; Eighth order; Error equation; Fifteenth order; Fourteenth order; Penta parametric family

Indexed keywords

EFFICIENCY INDEX; EIGHTH-ORDER; ERROR CONSTANT; ERROR EQUATION; FIFTEENTH-ORDER; FOURTEENTH-ORDER; PARAMETRIC FAMILY;

ALGEBRA; ASYMPTOTIC ANALYSIS;

NONLINEAR EQUATIONS;

EID: 77957995805     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2010.07.029     Document Type: Article

References (12)

1. Lars V. Ahlfors Complex Analysis 1979 McGraw-Hill Book, Inc.
2. W. Bi, H. Ren, and Q. Wu Three-step iterative methods with eighth-order convergence for solving nonlinear equations Journal of Computational and Applied Mathematics 225 2009 105 112
3. W. Bi, Q. Wu, and H. Ren A new family of eighth-order iterative methods for solving nonlinear equations Applied Mathematics and Computation 214 2009 236 245
4. Y.H. Geum, and Y.I. Kim A multi-parameter family of three-step eighth-order iterative methods locating a simple root Applied Mathematics and Computation 215 2010 3375 3382
5. P. Jarratt Some fourth-order multipoint iterative methods for solving equations Mathematics of Computation 20 95 1966 434 437
6. R. King A family of fourth-order methods for nonlinear equations SIAM Journal of Numerical Analysis 10 5 1973 876 879
7. H.T. Kung, and J.F. Traub Optimal order of one-point and multipoint iteration Journal of the Association for Computing Machinery 21 1974 643 651
8. L. Liu, and X. Wang Eighth-order methods with high efficiency index for solving nonlinear equations Applied Mathematics and Computation 215 2010 3449 3454
9. B. Neta On a family of Multipoint Methods for Non-linear Equations International Journal of Computer Mathematics 9 1981 353 361
10. J.F. Traub Iterative Methods for the Solution of Equations 1982 Chelsea Publishing Company
11. X. Wang, and L. Liu Modified Ostrowski's method with eighth-order convergence and high efficiency index Applied Mathematics Letters 23 2010 549 554
12. Stephen Wolfram The Mathematica Book 5th ed. 2003 Wolfram Media