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JF Traub (1964)
Iterative Methods for the Solution of Equations
L Fousse, G Hanrot, V Lefèvre, P Pélissier, P Zimmermann (2007)
MPFR: a multiple-precision binary floating-point library with correct roundingACM Trans. Math. Softw., 33
AM Ostrowski (1960)
Solutions of Equations and System of Equations
A Genocchi (1869)
Relation entre la différence et la dérivée d’un même ordre quelconqueArch. Math. Phys., I
JF Steffensen (1933)
Remarks on iterationSkand Aktuar Tidsr., 16
JR Sharma, H Arora (2014)
A novel derivative free algorithm with seventh order convergence for solving systems of nonlinear equationsNumer. Algor., 4
X Wang, T Zhang, W Qian, M Teng (2015)
Seventh-order derivative-free iterative method for solving nonlinear systemsNumer. Algor., 70
M Grau-Sánchez, À Grau, M Noguera (2011)
Frozen divided difference scheme for solving systems of nonlinear equationsJ. Comput. Appl. Math., 235
M Grau-Sánchez, M Noguera, S Amat (2013)
On the approximation of derivatives using divided difference operators preserving the local convergence order of iterative methodsJ. Comput. Appl. Math., 237
JR Sharma, H Arora (2016)
Efficient derivative-free numerical methods for solving systems of nonlinear equationsComp. Appl. Math., 35
JR Sharma, H Arora (2013)
An efficient derivative free iterative method for solving systems of nonlinear equationsAppl. Anal. Discrete Math., 7
Q Zheng, P Zhao, F Huang (2011)
A family of fourth-order Steffensen-type methods with the applications on solving nonlinear ODEsAppl. Math. Comput., 217
H Ren, Q Wu, W Bi (2009)
A class of two-step Steffensen type methods with fourth-order convergenceAppl. Math. Comput., 209
JR Sharma, P Gupta (2014)
Efficient Family of Traub-Steffensen-Type Methods for Solving Systems of Nonlinear Equations. Advances in Numerical Analysis. Article ID 152187
V Alarcón, S Amat, S Busquier, DJ López (2008)
A Steffensen’s type method in Banach spaces with applications on boundary-value problemsJ. Comput. Appl. Math., 216
A Cordero, JL Hueso, E Martínez, JR Torregrosa (2010)
A modified Newton-Jarratt’s compositionNumer. Algor., 55
LO Jay (2001)
A note on Q-order of convergenceBIT, 41
FA Potra, V Pták (1984)
Nondiscrete Induction and Iterarive Processes
X Wang, T Zhang (2013)
A family of Steffensen type methods with seventh-order convergenceNumer. Algor., 62
C Hermite (1878)
Sur la formule d’interpolation de LagrangeJ. Reine Angew. Math., 84
Z Liu, Q Zheng, P Zhao (2010)
A variant of Steffensen’s method of fourth-order convergence and its applicationsAppl. Math. Comput., 216
We present a three-step two-parameter family of derivative free methods with seventh-order of convergence for solving systems of nonlinear equations numerically. The proposed methods require evaluation of two central divided differences and inversion of only one matrix per iteration. As a result, the proposed family is more efficient as compared with the existing methods of same order. Numerical examples show that the proposed methods produce approximations of greater accuracy and remarkably reduce the computational time for solving systems of nonlinear equations.
Numerical Algorithms – Springer Journals
Published: Jan 12, 2017
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