García-Olivo, M.; Gutiérrez, José M.; Magreñán, Á. A. A first overview on the real dynamics of Chebyshev’s method. (English) Zbl 1357.65054 J. Comput. Appl. Math. 318, 422-432 (2017). MSC: 65H04 PDFBibTeX XMLCite \textit{M. García-Olivo} et al., J. Comput. Appl. Math. 318, 422--432 (2017; Zbl 1357.65054) Full Text: DOI
Cordero, Alicia; Gutiérrez, José M.; Magreñán, Á. Alberto; Torregrosa, Juan R. Stability analysis of a parametric family of iterative methods for solving nonlinear models. (English) Zbl 1410.65183 Appl. Math. Comput. 285, 26-40 (2016). MSC: 65H10 PDFBibTeX XMLCite \textit{A. Cordero} et al., Appl. Math. Comput. 285, 26--40 (2016; Zbl 1410.65183) Full Text: DOI
Gutiérrez, J. M.; Hernández, L. J.; Magreñán, Á. A.; Rivas, M. T. Measures of the basins of attracting \(n\)-cycles for the relaxed Newton’s method. (English) Zbl 1353.65041 Amat, Sergio (ed.) et al., Advances in iterative methods for nonlinear equations. Cham: Springer (ISBN 978-3-319-39227-1/hbk; 978-3-319-39228-8/ebook). SEMA SIMAI Springer Series 10, 211-245 (2016). MSC: 65H05 65E05 30C15 PDFBibTeX XMLCite \textit{J. M. Gutiérrez} et al., SEMA SIMAI Springer Ser. 10, 211--245 (2016; Zbl 1353.65041) Full Text: DOI
Yakoubsohn, J.-C.; Gutiérrez, J. M.; Magreñán, Á. A. Complexity of an homotopy method at the neighbourhood of a zero. (English) Zbl 1406.65041 Amat, Sergio (ed.) et al., Advances in iterative methods for nonlinear equations. Cham: Springer (ISBN 978-3-319-39227-1/hbk; 978-3-319-39228-8/ebook). SEMA SIMAI Springer Series 10, 147-171 (2016). MSC: 65J15 PDFBibTeX XMLCite \textit{J. C. Yakoubsohn} et al., SEMA SIMAI Springer Ser. 10, 147--171 (2016; Zbl 1406.65041) Full Text: DOI
García-Olivo, Martín; Gutiérrez, José M.; Alberto Magreñán, Á. A complex dynamical approach of Chebyshev’s method. (English) Zbl 1327.65096 S\(\vec{\text{e}}\)MA J. 71, No. 1, 57-68 (2015). MSC: 65H05 65H04 65E05 30C15 PDFBibTeX XMLCite \textit{M. García-Olivo} et al., S\(\vec{\text{e}}\)MA J. 71, No. 1, 57--68 (2015; Zbl 1327.65096) Full Text: DOI
Magreñán, Ángel Alberto; Gutiérrez, José Manuel Real dynamics for damped Newton’s method applied to cubic polynomials. (English) Zbl 1345.65032 J. Comput. Appl. Math. 275, 527-538 (2015). MSC: 65H04 37D45 37M05 PDFBibTeX XMLCite \textit{Á. A. Magreñán} and \textit{J. M. Gutiérrez}, J. Comput. Appl. Math. 275, 527--538 (2015; Zbl 1345.65032) Full Text: DOI
Magreñán, Ángel Alberto; Cordero, Alicia; Gutiérrez, José M.; Torregrosa, Juan R. Real qualitative behavior of a fourth-order family of iterative methods by using the convergence plane. (English) Zbl 07312639 Math. Comput. Simul. 105, 49-61 (2014). MSC: 37-XX 65-XX PDFBibTeX XMLCite \textit{Á. A. Magreñán} et al., Math. Comput. Simul. 105, 49--61 (2014; Zbl 07312639) Full Text: DOI Link
Argyros, Ioannis Konstantinos; Gutiérrez, José Manuel; Magreñán, Ángel Alberto; Romero, Natalia Convergence of the relaxed Newton’s method. (English) Zbl 1286.65067 J. Korean Math. Soc. 51, No. 1, 137-162 (2014). Reviewer: Werner H. Schmidt (Greifswald) MSC: 65J15 47H30 47J25 65R20 45G10 PDFBibTeX XMLCite \textit{I. K. Argyros} et al., J. Korean Math. Soc. 51, No. 1, 137--162 (2014; Zbl 1286.65067) Full Text: DOI Link
Gutiérrez, J. M.; Magreñán, Á. A.; Romero, N. On the semilocal convergence of Newton-Kantorovich method under center-Lipschitz conditions. (English) Zbl 1329.65101 Appl. Math. Comput. 221, 79-88 (2013). MSC: 65H05 PDFBibTeX XMLCite \textit{J. M. Gutiérrez} et al., Appl. Math. Comput. 221, 79--88 (2013; Zbl 1329.65101) Full Text: DOI
Gutiérrez, José Manuel; Magreñán, Ángel Alberto; Varona, Juan Luis The “Gauss-Seidelization” of iterative methods for solving nonlinear equations in the complex plane. (English) Zbl 1243.65052 Appl. Math. Comput. 218, No. 6, 2467-2479 (2011). MSC: 65H05 65E05 PDFBibTeX XMLCite \textit{J. M. Gutiérrez} et al., Appl. Math. Comput. 218, No. 6, 2467--2479 (2011; Zbl 1243.65052) Full Text: DOI