| Title:
|
Local convergence analysis of a modified Newton-Jarratt's composition under weak conditions (English) |
| Author:
|
Argyros, Ioannis K. |
| Author:
|
George, Santhosh |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
60 |
| Issue:
|
2 |
| Year:
|
2019 |
| Pages:
|
219-229 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A. Cordero et. al (2010) considered a modified Newton-Jarratt's composition to solve nonlinear equations. In this study, using decomposition technique under weaker assumptions we extend the applicability of this method. Numerical examples where earlier results cannot apply to solve equations but our results can apply are also given in this study. (English) |
| Keyword:
|
Newton-Jarratt's method |
| Keyword:
|
radius of convergence |
| Keyword:
|
local convergence |
| Keyword:
|
decomposition techniques |
| Keyword:
|
restricted convergence domain |
| MSC:
|
41A25 |
| MSC:
|
49M15 |
| MSC:
|
65D10 |
| MSC:
|
65D99 |
| MSC:
|
65J20 |
| MSC:
|
74G20 |
| idZBL:
|
Zbl 07144891 |
| idMR:
|
MR3982470 |
| DOI:
|
10.14712/1213-7243.2019.005 |
| . |
| Date available:
|
2019-08-05T09:49:16Z |
| Last updated:
|
2021-07-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147815 |
| . |
| Reference:
|
[1] Amat S., Busquier S., Negra M.: Adaptive approximation of nonlinear operators.Numer. Funct. Anal. Optim. 25 (2004), no. 5–6, 397–405. Zbl 1071.65077, MR 2106266, 10.1081/NFA-200042628 |
| Reference:
|
[2] Argyros I. K.: Computational Theory of Iterative Methods.Studies in Computational Mathematics, 15, Elsevier, Amsterdam, 2007. Zbl 1147.65313, MR 2356038 |
| Reference:
|
[3] Argyros I. K., Cho Y. J., George S.: Local convergence for some third-order iterative methods under weak conditions.J. Korean Math. Soc. 53 (2016), no. 4, 781–793. MR 3521238, 10.4134/JKMS.j150244 |
| Reference:
|
[4] Argyros I. K., George S.: Ball convergence of a sixth order iterative method with one parameter for solving equations under weak conditions.Calcolo 53 (2016), no. 4, 585–595. MR 3574604, 10.1007/s10092-015-0163-y |
| Reference:
|
[5] Argyros I. K., Magreñán Á. A.: Local convergence analysis of proximal Gauss-Newton method for penalized nonlinear least squares problems.Appl. Math. Comput. 241 (2014), 401–408. MR 3223438 |
| Reference:
|
[6] Argyros I. K., Szidarovszky F.: The Theory and Applications of Iteration Methods.Systems Engineering Series, CRC Press, Boca Raton, 1993. MR 1272012 |
| Reference:
|
[7] Cordero A., Hueso J., Martinez E., Torregrosa J. R.: A modified Newton-Jarratt's composition.Numer. Algorithms 55 (2010), no. 1, 87–99. MR 2679752, 10.1007/s11075-009-9359-z |
| Reference:
|
[8] Cordero A., Torregrosa J. R.: Variants of Newton's method for functions of several variables.Appl. Math. Comput. 183 (2006), no. 1, 199–208. MR 2282802 |
| Reference:
|
[9] Cordero A., Torregrosa J. R.: Variants of Newton's method using fifth-order quadrature formulas.Appl. Math. Comput. 190 (2007), no. 1, 686–698. MR 2338747 |
| Reference:
|
[10] Ezquerro J. A., Hernández M. A., Romero A. N.: Approximacion de soluciones de algunas equacuaciones integrals de Hammerstein mediante metodos iterativos tipo.Newton, XXI Congresode ecuaciones diferenciales y aplicaciones Universidad de Castilla-La Mancha, Ciudad Real, 2009, 8 pages. |
| Reference:
|
[11] Grau-Sánchez M., Grau À., Noguera M.: On the computational efficiency index and some iterative methods for solving systems of non-linear equations.J. Comput. Appl. Math. 236 (2011), no. 6, 1259–1266. MR 2854048, 10.1016/j.cam.2011.08.008 |
| Reference:
|
[12] Gutiérrez J. M., Hernández M. A.: Newton's method under weak Kantorovich conditions.IMA J. Numer. Anal. 20 (2000), no. 4, 521–532. MR 1795296, 10.1093/imanum/20.4.521 |
| Reference:
|
[13] Homeier H. H. H.: A modified Newton method with cubic convergence, the multivariate case.J. Comput. Appl. Math. 169 (2004), no. 1, 161–169. MR 2071267, 10.1016/j.cam.2003.12.041 |
| Reference:
|
[14] Homeier H. H. H.: On Newton-type methods with cubic convergence.J. Comput. Appl. Math. 176 (2005), no. 2, 425–432. MR 2116403, 10.1016/j.cam.2004.07.027 |
| Reference:
|
[15] Kou J., Li Y., Wang X.: Some modification of Newton's method with fifth-order convergence.J. Comput. Appl. Math. 209 (2007), no. 2, 146–152. MR 2387121, 10.1016/j.cam.2006.10.072 |
| Reference:
|
[16] Noor M. A., Waseem M.: Some iterative methods for solving a system of nonlinear equations.Comput. Math. Appl. 57 (2009), no. 1, 101–106. MR 2484261, 10.1016/j.camwa.2008.10.067 |
| Reference:
|
[17] Ren H., Argyros I. K.: Improved local analysis for a certain class of iterative methods with cubic convergence.Numer. Algorithms 59 (2012), no. 4, 505–521. MR 2892562, 10.1007/s11075-011-9501-6 |
| Reference:
|
[18] Rheinboldt W. C.: An adaptive continuation process for solving systems of nonlinear equations.Mathematical models and numerical methods, Banach Center Publ., 3, PWN, Warszawa, 1978, pages 129–142. Zbl 0378.65029, MR 0514377 |
| Reference:
|
[19] Shah F. A., Noor M. A.: Some numerical methods for solving nonlinear equations by using decomposition technique.Appl. Math. Comput. 251 (2015), 378–386. MR 3294725 |
| Reference:
|
[20] Sharma J. R., Gupta P.: An efficient fifth order method for solving systems of nonlinear equations.Comput. Math. Appl. 67 (2014), no. 3, 591–601. MR 3149734, 10.1016/j.camwa.2013.12.004 |
| Reference:
|
[21] Traub J. F.: Iterative Methods for the Solution of Equations.AMS Chelsea Publishing, New York, 1982. Zbl 0672.65025 |
| . |
