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dc.contributor.author | Budzko, Dzmitry | es_ES |
dc.contributor.author | Cordero Barbero, Alicia | es_ES |
dc.contributor.author | Torregrosa Sánchez, Juan Ramón | es_ES |
dc.date.accessioned | 2016-06-06T07:13:47Z | |
dc.date.available | 2016-06-06T07:13:47Z | |
dc.date.issued | 2014-11 | |
dc.identifier.issn | 2254-3902 | |
dc.identifier.uri | http://hdl.handle.net/10251/65274 | |
dc.description.abstract | The paper is devoted to description of certain ways of extending the domain of convergence of Newton’s method. This paper is a survey of contributions of representatives of Soviet and Russian mathematical school, namely, Kalitkin, Puzynin, Madorskij and others. They introduced different kinds of damping multiplier and showed that their usage may be helpful and beneficial while solving different nonlinear equations and systems starting with “bad” zero estimate. We have also paid attention to the problem of degeneracy of Jacobian matrix and the ways it was solved by named researchers. Finally, we have tested the presented iterative schemes on some examples in order to check their effectiveness. All complete strict proofs of key theorems can be found both in Russian and English in the provided bibliography | es_ES |
dc.language | Inglés | es_ES |
dc.publisher | Springer | es_ES |
dc.relation.ispartof | Journal of the Spanish Society of Applied Mathematics | es_ES |
dc.rights | Reserva de todos los derechos | es_ES |
dc.subject | Nonlinear equations | es_ES |
dc.subject | Newton method | es_ES |
dc.subject | Damping multiplier | es_ES |
dc.subject | Convergence domain | es_ES |
dc.subject | Regularization | es_ES |
dc.subject.classification | MATEMATICA APLICADA | es_ES |
dc.title | Modifications of Newton's method to extend the convergence domain | es_ES |
dc.type | Artículo | es_ES |
dc.identifier.doi | 10.1007/s40324-014-0020-y | |
dc.rights.accessRights | Cerrado | es_ES |
dc.contributor.affiliation | Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada | es_ES |
dc.contributor.affiliation | Universitat Politècnica de València. Instituto Universitario de Matemática Multidisciplinar - Institut Universitari de Matemàtica Multidisciplinària | es_ES |
dc.description.bibliographicCitation | Budzko, D.; Cordero Barbero, A.; Torregrosa Sánchez, JR. (2014). Modifications of Newton's method to extend the convergence domain. Journal of the Spanish Society of Applied Mathematics. 66(1):43-53. doi:10.1007/s40324-014-0020-y | es_ES |
dc.description.accrualMethod | S | es_ES |
dc.relation.publisherversion | http://dx.doi.org/10.1007/s40324-014-0020-y | es_ES |
dc.description.upvformatpinicio | 43 | es_ES |
dc.description.upvformatpfin | 53 | es_ES |
dc.type.version | info:eu-repo/semantics/publishedVersion | es_ES |
dc.description.volume | 66 | es_ES |
dc.description.issue | 1 | es_ES |
dc.relation.senia | 282657 | es_ES |
dc.description.references | Aleksandrov, L.: The Newton-Kantorovich regularized computing processes. USSR Comput. Math. Math. Phys. 11(1), 46–57 (1971) | es_ES |
dc.description.references | Amat, S., Busquier, S.: On a higher order secant method. Appl. Math. Comput. 141(2–3), 321–329 (2003) | es_ES |
dc.description.references | Amat, S., Busquier, S., Magreñan, A.A.: Reducing chaos and bifurcations in Newton-type methods. Abstr. Appl. Anal. 726701, 10 (2013) | es_ES |
dc.description.references | Argyros, I.K., Hilout, S.: On the semilocal convergence of damped Newton’s method. Appl. Math. Comput. 219, 2808–2824 (2012) | es_ES |
dc.description.references | Argyros, I.K., Gutiérrez, J.M., Magreñán, Á.A., Romero, N.: Convergence of the relaxed Newton’s method. J. Korean. Math. Soc. 51(1), 137–162 (2014) | es_ES |
dc.description.references | Babajee, D.K.R., Cordero, A., Soleymani, F., Torregrosa, J.R.: On improved three-step schemes with high efficiency index and their dynamics. Numer. Algorithms 65, 153–169 (2014) | es_ES |
dc.description.references | Cordero, A., Lotfi, T., Mahdiani, K., Torregrosa, J.R.: Two optimal general classes of iterative methods with eight-order. Acta Appl. Math. doi: 10.1007/s10440-014-9869-0 | es_ES |
dc.description.references | Cordero, A., Torregrosa, J.R.: A class of Steffensen type methods with optimal order of convergence. Appl. Math. Comput. 217, 7653–7659 (2011) | es_ES |
dc.description.references | Dembo, R.S., Eisenstat, S.C., Steihaug, T.: Inexact newton methods. SIAM J. Numer. Anal. 19, 400–408 (1982) | es_ES |
dc.description.references | Dennis, J.E., Jr. Schnabel, R.B.: Numerical methods for unconstrained optimization and nonlinear equations. Classics in applied mathematics, vol. 16. SIAM (1996) | es_ES |
dc.description.references | Ermakov, V.V., Kalitkin, N.N.: The optimal step and regularization for Newton’s method. USSR Comput. Math. Math. Phys. 21(2), 235–242 (1981) | es_ES |
dc.description.references | Ezquerro, J.A., Hernández, M.A., Romero, N.: On some one-point hybrid iterative methods. Original Res. Art. Nonlinear Anal. Theory Methods Appl. 72(2), 587–601 (2010) | es_ES |
dc.description.references | Gavurin, M.K.: Nonlinear functional equations and continuous analogues of iteration methods. Izvestiya Vysshikh Uchebnykh Zavedenii Matematika 5, 18–31 (1958) | es_ES |
dc.description.references | Hernández, M.A., Romero, N.: A uniparametric family of iterative processes for solving nondifferentiable equations. J. Math. Annal. Appl. 275, 821–834 (2002) | es_ES |
dc.description.references | Kalitkin, N.N., et al.: Mathematical Models in Nature and Science. Moscow (2005, in Russian) | es_ES |
dc.description.references | Kalitkin, N.N., Poshivailo, I.P.: Computation of simple and multiple roots of a nonlinear equation. Math. Models Comput. Simul. 1(4), 514–520 (2009) | es_ES |
dc.description.references | Kalitkin, N.N., Kuz’mina, L.V.: Computation of roots of an equation and determination of their multiplicity. Math. Models Comput. Simul. 3(1), 65–80 (2011) | es_ES |
dc.description.references | Kung, H.T., Traub, J.F.: Optimal order of one-point and multi-point iteration. J. Assoc. Comput. Mach. 21, 643–651 (1974) | es_ES |
dc.description.references | Madorskij, V.M.: Quasi-Newtonian Processes for Solving Nonlinear Equations. Brest State University, Brest (2005, in Russian) | es_ES |
dc.description.references | Magreñán, Á.A.: Estudio de la dinámica del método de Newton amortiguado. PhD Thesis University of La Rioja, Spain. http://dialnet.unirioja.es/servlet/tesis?codigo=38821 (2013) | es_ES |
dc.description.references | More, J.J., Garbow, B.S., Hillstrom, K.E.: Testing unconstrained optimization software. ACM Trans. Math. Softw. 7(1), 17–41 (1981) | es_ES |
dc.description.references | Ostrowski, A.M.: Solutions of Equations and Systems of Equations. Academic Press, New York-London (1966) | es_ES |
dc.description.references | Puzynin, I.V., Zhanlav, T.: Convergence of iterations on the basis of a continuous analogue of the Newton method. Comput. Math. Math. Phys. 32(6), 729–737 (1992) | es_ES |
dc.description.references | Puzynin, I.V., et al.: The generalized continuous analog of Newton’s method for the numerical study of some nonlinear quantum-field models. Phys. Part. Nucl. 30, 87 (1999) | es_ES |
dc.description.references | Tikhonov, A.N.: Regularization of incorrectly posed problems. Soviet Math. Dokl. 4, 6 (1963) | es_ES |
dc.description.references | Tikhonov, A.N.: The stability of algorithms for the solution of degenerate systems of linear algebraic equations. USSR Comput. Math. Math. Phys. 5(4), 181–188 (1965) | es_ES |
dc.description.references | Tikhonov, A.N., Arsenin, V.Y.: Methods for Solving Ill-Posed Problems. John Wiley and Sons Inc, New York (1977) | es_ES |
dc.description.references | Velasco Del Olmo, A.I.: Mejoras de los dominios de puntos de salida de métodos iterativos que no utilizan derivadas. PhD University of La Rioja, Spain. http://dialnet.unirioja.es/servlet/tesis?codigo=38218 (2013) | es_ES |
dc.description.references | Ypma, T.J.: Local convergence of inexact Newton methods. SIAM J. Numer. Anal. 21, 583–590 (1984) | es_ES |
dc.description.references | Zhidkov, E.P., Makarenko, G.J., Puzynin, I.V.: Continuous analogue of Newton’s method in nonlinear problems of physics. Phys. Part. Nuclei. 4(1), 127–166 (1973). (in Russian) | es_ES |