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Abstrakty
This paper considers various hybrid methods for solving a system of nonlinear equations. Extensive numerical experiments confirm the research hypothesis that one particular form of hybridization of the conjugate gradient algorithm with Newton’s method outperforms other hybrid strategies considered in the paper.
Czasopismo
Rocznik
Tom
Strony
269--289
Opis fizyczny
Bibliogr. 16 poz., rys., tab.
Twórcy
autor
- University of Turku, Department of Mathematics and Statistics, 20014 Vesilinnantie 5, Turku, Finland
autor
- University of Turku, Department of Mathematics and Statistics, 20014 Vesilinnantie 5, Turku, Finland
autor
- University of Turku, Department of Mathematics and Statistics, 20014 Vesilinnantie 5, Turku, Finland
Bibliografia
- Andrei, N. (2008) An Unconstrained Optimization Test Functions Collection, Advanced Modeling and Optimization, 10, 147–161.
- Atkinson, K. E. (1978) An Introduction to Numerical Analysis. Nonlinear Systems of Equations. John Wiley & Sons, Canada.
- Broyden, C. G. (1970) ”The convergence of a class of double-rank minimization algorithms”, Journal of the Institute of Mathematics and Its Applications, 6: 76–90, doi:10.1093/imamat/6.1.76
- Buckley, A. (1978) A combined conjugate-gradient quasi-Newton minimization algorithm. Mathematical Programming, 15, 200–210.
- Burden, R. L. and Faires, J.D. (2010) Numerical Analysis, 9th Edition. Brooks Cole.
- Hestenes, M. and Stiefel, E. (1952) Methods of Conjugate Gradients for Solving Linear Systems. Journal of Research of the National Bureau of Standards, 49, 409–436.
- Fletcher, R. (1970) ”A New Approach to Variable Metric Algorithms”, Computer Journal, 13 (3): 317–322, doi:10.1093/comjnl/13.3.317
- Fletcher, R. and Reeves, C. (1964) Function Minimization by Conjugate Gradients. Computer Journal, 7, 149–154.
- Goldfarb, D. (1970) ”A Family of Variable Metric Updates Derived by Variational Means”, Mathematics of Computation, 24 (109): 23–26, doi:10.1090/S0025-5718-1970-0258249-6
- Kelley, C. (1987) Solving Nonlinear Equations with Newton’s Method. Cambridge University Press.
- Kelley, C. (1995) Iterative Methods for Linear and Nonlinear Equations. Society for Industrial and Applied Mathematics, Philadelphia.
- Nedzhibov, G. (2008) A family of multi-point iterative methods for solving systems of nonlinear equations. Journal of Computational and Applied Mathematics, 2, 244-250.
- Powell, M. J. D. (1970) A hybrid method for nonlinear equations. Numerical Methods for Nonlinear Algebraic Equations, ch. 6, 87–114.
- Shanno, David F. (July 1970) ”Conditioning of quasi-Newton methods for function minimization”, Mathematics of Computation, 24 (111): 647–656, doi:10.1090/S0025-5718-1970-0274029-X, MR 0274029
- Shi, Y. (2000) Globally Convergent Algorithms for Unconstrained Optimization. Computational Optimization and Applications, New York, 16, 295–308.
- Taheri, S. and Mammadov, M. (2012) Solving systems of nonlinear equations using a globally Convergent Optimization algorithm. Global Journal of Technology & Optimization, 3, 132–138.
Typ dokumentu
Bibliografia
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bwmeta1.element.baztech-14801b99-a8b9-4853-910d-7367eb95fc1c
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