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Advances in Numerical Analysis
Volume 2013 (2013), Article ID 252798, 11 pages
On Some Efficient Techniques for Solving Systems of Nonlinear Equations
1Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal, Punjab 148106, India
2Department of Mathematics, Government Ranbir College, Sangrur, Punjab 148001, India
Received 18 June 2013; Revised 3 September 2013; Accepted 4 September 2013
Academic Editor: Zhangxing Chen
Copyright © 2013 Janak Raj Sharma and Puneet Gupta. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- A. M. Ostrowski, Solution of Equations and Systems of Equations, Academic Press, New York, NY, USA, 1966.
- J. M. Ortega and W. C. Rheinboldt, Iterative Solutions of Nonlinear Equations in Several Variables, Academic Press, New York, NY, USA, 1970.
- F. A. Potra and V. Pták, Nondiscrete Induction and Iterarive Processes, Pitman, Boston, Mass, USA, 1984.
- C. T. Kelley, Solving Nonlinear Equations with Newton's Method, SIAM, Philadelphia, Pa, USA, 2003.
- J. F. Traub, Iterative Methods for the Solution of Equations, Prentice-Hall, Englewood Cliffs, NJ, USA, 1964.
- J. M. Gutiérrez and M. A. Hernández, “A family of chebyshev-halley type methods in banach spaces,” Bulletin of the Australian Mathematical Society, vol. 55, no. 1, pp. 113–130, 1997.
- M. Palacios, “Kepler equation and accelerated Newton method,” Journal of Computational and Applied Mathematics, vol. 138, no. 2, pp. 335–346, 2002.
- S. Amat, S. Busquier, and J. M. Gutiérrez, “Geometric constructions of iterative functions to solve nonlinear equations,” Journal of Computational and Applied Mathematics, vol. 157, no. 1, pp. 197–205, 2003.
- M. Frontini and E. Sormani, “Third-order methods from quadrature formulae for solving systems of nonlinear equations,” Applied Mathematics and Computation, vol. 149, no. 3, pp. 771–782, 2004.
- H. H. H. Homeier, “A modified Newton method with cubic convergence: the multivariate case,” Journal of Computational and Applied Mathematics, vol. 169, no. 1, pp. 161–169, 2004.
- M. T. Darvishi and A. Barati, “A fourth-order method from quadrature formulae to solve systems of nonlinear equations,” Applied Mathematics and Computation, vol. 188, no. 1, pp. 257–261, 2007.
- A. Cordero and J. R. Torregrosa, “Variants of Newton's Method using fifth-order quadrature formulas,” Applied Mathematics and Computation, vol. 190, no. 1, pp. 686–698, 2007.
- M. A. Noor and M. Waseem, “Some iterative methods for solving a system of nonlinear equations,” Computers and Mathematics with Applications, vol. 57, no. 1, pp. 101–106, 2009.
- A. Cordero, E. Martínez, and J. R. Torregrosa, “Iterative methods of order four and five for systems of nonlinear equations,” Journal of Computational and Applied Mathematics, vol. 231, no. 2, pp. 541–551, 2009.
- A. Cordero, J. L. Hueso, E. Martínez, and J. R. Torregrosa, “A modified Newton-Jarratt's composition,” Numerical Algorithms, vol. 55, no. 1, pp. 87–99, 2010.
- M. Grau-Sánchez, Á. Grau, and M. Noguera, “On the computational efficiency index and some iterative methods for solving systems of nonlinear equations,” Journal of Computational and Applied Mathematics, vol. 236, no. 6, pp. 1259–1266, 2011.
- M. Grau-Sánchez, À. Grau, and M. Noguera, “Ostrowski type methods for solving systems of nonlinear equations,” Applied Mathematics and Computation, vol. 218, no. 6, pp. 2377–2385, 2011.
- J. R. Sharma, R. K. Guha, and R. Sharma, “An efficient fourth order weighted-Newton method for systems of nonlinear equations,” Numerical Algorithms, vol. 62, no. 2, pp. 307–323, 2013.
- S. Wolfram, The Mathematica Book, Wolfram Media, Champaign, Ill, USA, 5th edition, 2003.
- M. S. Petković, “Remarks on ‘on a general class of multipoint root-finding methods of high computational efficiency’,” SIAM Journal on Numerical Analysis, vol. 49, no. 3, pp. 1317–1319, 2011.
- L. Fousse, G. Hanrot, V. Lefèvre, P. Pélissier, and P. Zimmermann, “MPFR: a multiple-precision binary floating-point library with correct rounding,” ACM Transactions on Mathematical Software, vol. 33, no. 2, Article ID 1236468, p. 15, 2007.