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http://dx.doi.org/10.14317/jami.2014.747

A HIGHER ORDER ITERATIVE ALGORITHM FOR MULTIVARIATE OPTIMIZATION PROBLEM  

Chakraborty, Suvra Kanti (Department of Mathematics, Indian Institute of Technology)
Panda, Geetanjali (Department of Mathematics, Indian Institute of Technology)
Publication Information
Journal of applied mathematics & informatics / v.32, no.5_6, 2014 , pp. 747-760 More about this Journal
Abstract
In this paper a higher order iterative algorithm is developed for an unconstrained multivariate optimization problem. Taylor expansion of matrix valued function is used to prove the cubic order convergence of the proposed algorithm. The methodology is supported with numerical and graphical illustration.
Keywords
Matrix Taylor expansion; Kronecker product; Newton's method; Cubic order convergence;
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1 Alicia Cordero, Jose L Hueso, Eulalia Martinez, and Juan R Torregrosa, A family of iterative methods with sixth and seventh order convergence for nonlinear equations, Mathematical and Computer Modelling 52 (2010), no. 9, 1490-1496.   DOI   ScienceOn
2 John Brewer, Kronecker products and matrix calculus in system theory, Circuits and Systems, IEEE Transactions on 25 (1978), no. 9, 772-781.   DOI
3 Changbum Chun, A family of composite fourth-order iterative methods for solving non-linear equations, Applied mathematics and computation 187 (2007), no. 2, 951-956.   DOI   ScienceOn
4 Changbum Chun, Some fourth-order iterative methods for solving nonlinear equations, Applied Mathematics and Computation 195 (2008), no. 2, 454-459.   DOI   ScienceOn
5 Paul S. Dwyer and M.S. MacPhail, Symbolic matrix derivatives, The annals of mathematical statistics 19 (1948), no. 4, 517-534.   DOI
6 H.H.H. Homeier, A modified newton method for rootfinding with cubic convergence, Journal of Computational and Applied Mathematics 157 (2003), no. 1, 227-230.   DOI   ScienceOn
7 Jisheng Kou, Yitian Li, and Xiuhua Wang, A modification of newton method with third-order convergence, Applied Mathematics and Computation 181 (2006), no. 2, 1106-1111.   DOI   ScienceOn
8 Jisheng Kou, Yitian Li, and Xiuhua Wang, Some variants of ostrowski's method with seventh-order convergence, Journal of Computational and Applied Mathematics 209 (2007), no. 2, 153-159.   DOI   ScienceOn
9 Liping Liu and Xia Wang, Eighth-order methods with high efficiency index for solving nonlinear equations, Applied Mathematics and Computation 215 (2010), no. 9, 3449-3454.   DOI   ScienceOn
10 William J. Vetter, Derivative operations on matrices, Automatic Control, IEEE Transactions on 15 (1970), no. 2, 241-244.   DOI
11 Alfredo Martinez Estrada, A treatise on econometric forecasting, Ph.D. thesis, California Institute of Technology, 2007.
12 Eric Walter and Luc Pronzato, Identification of parametric models, Communications and Control Engineering (1997).
13 H.W. Turnbull, On differentiating a matrix, Proceedings of the Edinburgh Mathematical Society (Series 2) 1 (1928), no. 02, 111-128.
14 H.W. Turnbull, A matrix form of taylor's theorem, Proceedings of the Edinburgh Mathematical Society (Series 2) 2 (1930), no. 01, 33-54.
15 William J. Vetter, Matrix calculus operations and taylor expansions, SIAM review 15 (1973), no. 2, 352-369.   DOI   ScienceOn
16 Zhang Yimin, Suhuan Chen, Qiaoling Liu, and Tieqiang Liu, Stochastic perturbation finite elements, Computers & Structures 59 (1996), no. 3, 425-429.   DOI   ScienceOn
17 Yimin Zhang, Bangchun Wen, and Qiaoling Liu, Sensitivity analysis of rotor-stator systems with rubbing*, Mechanics of structures and machines 30 (2002), no. 2, 203-211.   DOI   ScienceOn
18 Y.M. Zhang, L. Zhang, J.X. Zheng, and B.C. Wen, Neural network for structural stress concentration factors in reliability-based optimization, Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 220 (2006), no. 3, 217-224.   DOI
19 Qi Zhao and Christian Bohn, A linearization free recursive prediction error method for combined state and parameter estimation for nonlinear systems, American Control Conference (ACC), 2013, IEEE, 2013, pp. 899-904.
20 H.H.H. Homeier, On newton-type methods with cubic convergence, Journal of Computational and Applied Mathematics 176 (2005), no. 2, 425-432.   DOI   ScienceOn