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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 875935, 6 pages
An Improved Diagonal Jacobian Approximation via a New Quasi-Cauchy Condition for Solving Large-Scale Systems of Nonlinear Equations
1Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia
2Department of Mathematical Sciences, Faculty of Science, Bayero University, Kano PMB 3011, Nigeria
3Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia
Received 8 August 2012; Revised 14 December 2012; Accepted 15 December 2012
Academic Editor: Turgut Öziş
Copyright © 2013 Mohammed Yusuf Waziri and Zanariah Abdul Majid. 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.
- J. E. Dennis, Jr. and R. B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice Hall, Englewood Cliffs, NJ, USA, 1983.
- C. T. Kelley, Iterative Methods for Linear and Nonlinear Equations, vol. 16, SIAM, Philadelphia, Pa, USA, 1995.
- W. J. Leong, M. A. Hassan, and M. Waziri Yusuf, “A matrix-free quasi-Newton method for solving large-scale nonlinear systems,” Computers & Mathematics with Applications, vol. 62, no. 5, pp. 2354–2363, 2011.
- D.-H. Li and M. Fukushima, “A modified BFGS method and its global convergence in nonconvex minimization,” Journal of Computational and Applied Mathematics, vol. 129, no. 1-2, pp. 15–35, 2001.
- B.-C. Shin, M. T. Darvishi, and C.-H. Kim, “A comparison of the Newton-Krylov method with high order Newton-like methods to solve nonlinear systems,” Applied Mathematics and Computation, vol. 217, no. 7, pp. 3190–3198, 2010.
- E. Spedicato, “Cumputational experience with quasi-Newton algorithms for minimization problems of moderatetly large size,” Tech. Rep. CISE-N-175 3, pp. 10–41, 1975.