Geodesic
Two new Newton-type methods for the nonlinear equations
Xie, Ya-Jun 1 ; Huang, Na 2 ; Ma, Chang-Feng2
1 College of Mathematics and Informatics, Fujian Key Laborotary of Mathematical Analysis and Applications, Fujian Normal Universit, Fuzhou, 350117, P. R. China;Department of Mathematics and Physics, Fujian Jiangxia University, Fuzhou 350108, P. R. China
2 College of Mathematics and Informatics, Fujian Key Laborotary of Mathematical Analysis and Applications, Fujian Normal University, Fuzhou, 350117, P. R. China
Journal of nonlinear sciences and its applications, Tome 11 (2018) no. 2, p. 252-262.

Voir la notice de l'article provenant de la source International Scientific Research Publications

In this paper, based on the classical Newton method and Halley method, we propose two new Newton methods for solving the systems of nonlinear equations. The convergence performances of the two new variants of Newton iteration method are analyzed in details. Some numerical experiments are also presented to demonstrate the feasibility and efficiency of the proposed methods.
DOI : 10.22436/jnsa.011.02.07
Classification : 65H10
Keywords: Systems of nonlinear equations, Newton iteration method, Armijo linear search, convergence analysis, numerical tests

Xie, Ya-Jun  1 ; Huang, Na  2 ; Ma, Chang-Feng 2

1 College of Mathematics and Informatics, Fujian Key Laborotary of Mathematical Analysis and Applications, Fujian Normal Universit, Fuzhou, 350117, P. R. China;Department of Mathematics and Physics, Fujian Jiangxia University, Fuzhou 350108, P. R. China
2 College of Mathematics and Informatics, Fujian Key Laborotary of Mathematical Analysis and Applications, Fujian Normal University, Fuzhou, 350117, P. R. China 
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Xie, Ya-Jun ; Huang, Na ; Ma, Chang-Feng. Two new Newton-type methods for the nonlinear equations. Journal of nonlinear sciences and its applications, Tome 11 (2018) no. 2, p. 252-262. doi : 10.22436/jnsa.011.02.07. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.011.02.07/

[1] An, H.-B.; Bai, Z.-Z. A globally convergent Newton-GMRES method for large sparse systems of nonlinear equations , Appl. Numer. Math., Volume 57 (2007), pp. 235-252 | DOI | Zbl

[2] Bai, Z.-Z.; A class of two-stage iterative methods for systems of weakly nonlinear equations, Numer. Algorithms, Volume 14 (1997), pp. 295-319 | DOI | Zbl

[3] Bai, Z.-Z.; Migallón, V.; Penadés, J.; D. B. Szyld Block and asynchronous two-stage methods for mildly nonlinear systems , Numer. Math., Volume 82 (1999), pp. 1-20 | DOI | Zbl

[4] Bai, Z.-Z.; Yang, X. On HSS-based iteration methods for weakly nonlinear systems, Appl. Numer. Math., Volume 59 (2009), pp. 2923-2936 | Zbl | DOI

[5] Burden, R. L.; J. D. Faires Numerical analysis , Thomson Learning, New York, 2001

[6] Dennis, J. E.; Schnabel, R. B. Numerical methods for unconstrained optimization and nonlinear equation, Prentice Hall, New Jersey, 1983

[7] Gao, F.; Yang, X.-J.; Zhang, Y.-F. Exact traveling wave solutions for a new nonlinear heat-transfer equation , Thermal Science , Volume 21 (2016), pp. 309-315

[8] Huang, N.; C.-F. Ma A regularized smoothing Newton method for solving SOCCPs based on a new smoothing C-function , Appl. Math. Comput., Volume 230 (2014), pp. 315-329

[9] C. T. Kelley Iterative methods for linear and nonlinear equations , Society for Industrial and Applied Mathematics (SIAM), Philadelphia, 1995

[10] Kelley, C. T. Solving Nonlinear Equations with Newton’s Method, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, 2003 | DOI

[11] Levin, Y.; Ben-Israelb, A. Directional Halley and Quasi-Halley Methods in n Variables , Stud. Comput. Math., Amsterdam, 2001 | Zbl | DOI

[12] Moré, J. J.; Grabow, B. S.; K. E. Hillstrom Testing unconstrained optimization software, ACM Trans. Math. Software, Volume 7 (1981), pp. 17-41 | DOI

[13] Narang, M.; Bhatia, S.; Kanwar, V. New two-parameter Chebyshev-Halley-like family of fourth and sixthorder methods for systems of nonlinear equations, Appl. Math. Comput., Volume 275 (2016), pp. 394-403 | DOI

[14] Narushima, Y.; Sagara, N.; Ogasawara, H. A smoothing Newton method with Fischer-Burmeister function for second-order cone complementarity problems, J. Optim. Theory Appl., Volume 149 (2011), pp. 79-101 | DOI

[15] G. H. Nedzhibov A family of multi-pointiterative methods for solving systems of nonlinear equations, J. Comput. Appl. Math., Volume 222 (2008), pp. 244-250 | DOI

[16] M. A. Noor New classes of iterative methods for nonlinear equations , Appl. Math. Comput., Volume 191 (2007), pp. 128-131 | DOI

[17] Noor, M. A.; Shah, F. A. A Family of Iterative Schemes for Finding Zeros of Nonlinear Equations having Unknown Multiplicity, Appl. Math. Inf. Sci., Volume 8 (2014), pp. 2367-2373

[18] Shah, F. A.; Noor, M. A. Higher order iterative schemes for nonlinear equations using decomposition technique, Appl. Math. Comput., Volume 266 (2015), pp. 414-423 | DOI

[19] Sun, J. Z.; J. K. Zhang Solving nonlinear systems of equations based on social cognitive optimization, Comput. Eng. Appl., Volume 44 (2008), pp. 42-46

[20] Traub, J. F. Iterative Methods for the Solution of Equations , Prentice Hall, Englewood, 1964

[21] Woodbury, M. A. Inverting modified matrices, Princeton University, Princeton, 1950

[22] Xiao, X.; Yin, H. A new class of methods with higher order of convergence for solving systems of nonlinear equations, Appl. Math. Comput., Volume 264 (2015), pp. 300-309 | DOI

[23] X.-J. Yang A new integral transform with an application in heat-transfer problem, Thermal Sci., Volume 20 (2016), pp. 677-681

[24] Yang, X.-J.; F. Gao New Technology for Solving Diffusion and Heat Equations , Thermal Sci., Volume 21 (2017), pp. 133-140

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