- -

Modifications of Newton's method to extend the convergence domain

RiuNet: Repositorio Institucional de la Universidad Politécnica de Valencia

Compartir/Enviar a

Citas

Estadísticas

  • Estadisticas de Uso

Modifications of Newton's method to extend the convergence domain

Mostrar el registro sencillo del ítem

Ficheros en el ítem

[Cerrado]
Nombre: -Torregrosa;Cordero ...
Tamaño: 422.9Kb
Formato: PDF
Descripción: Versión editorial
Solicitar una copia al autor
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


Este ítem aparece en la(s) siguiente(s) colección(ones)

Mostrar el registro sencillo del ítem