Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Bücher
Zeitschriften
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
MTZ-Fachkongress

Antriebe und Energiesysteme von morgen


Austausch von Automobil- und Energiewirtschaft

Am 14./15. Mai geht es in Chemnitz um die Mobilitätswende durch Elektro- und Wasserstofffahrzeuge.
Erweiterte Suche
Anmelden
nach oben
Numerical Algorithms
Erschienen in: Numerical Algorithms 3/2020

17.12.2019 | Original Paper

Modified Newton-DSS method for solving a class of systems of nonlinear equations with complex symmetric Jacobian matrices

verfasst von: Fang Xie, Rong-Fei Lin, Qing-Biao Wu

Erschienen in: Numerical Algorithms | Ausgabe 3/2020

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

Double-step scale splitting (DSS) iteration method is proved to be an unconditionally convergent iteration method, which is also efficient and robust for solving a class of large sparse complex symmetric systems of linear equations. In this paper, by making use of the DSS iteration technique as the inner solver to approximately solve the Newton equations, we establish a new modified Newton-DSS method for solving systems of nonlinear equations whose Jacobian matrices are large, sparse, and complex symmetric. Subsequently, we investigate the local and semilocal convergence properties of our method under some proper assumptions. Finally, numerical results on some problems illustrate the superiority of our method over some previous methods.
Vorheriger Artikel Two-Level method for the total fractional-order variation model in image deblurring problem
Nächster Artikel A note on generalized averaged Gaussian formulas for a class of weight functions

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren
Literatur
1.
Bohr, T., Hensen, M.H., Paladin, G., Vulpiani, A.: Dynamical Systems Approach to Turbulence. Cambridge University Press, Cambridge (1998)CrossRef
2.
Sulem, C., Sulem, P.L.: The Nonlinear Schrödinger Equation, Self-focusing and Wave Collapse. Springer, New York (1999)MATH
3.
Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Rev. Mod. Phys. 74, 99–143 (2002)MathSciNetCrossRef
4.
Kuramoto, Y.: Oscillations, Chemical Waves, and Turbulence. Dover, Mineola (2003)MATH
5.
Dembo, R.S., Eisenstat, S.C., Steihaug, T.: Inexact Newton methods. SIAM J. Numer. Anal. 19, 400–408 (1982)MathSciNetCrossRef
6.
Saad, Y.: Iterative Methods for Sparse Linear Systems, 2nd edn. SIAM, Philadelphia (2003)CrossRef
7.
Bai, Z.Z., Golub, G.H., Ng, M.K.: Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems. SIAM J. Matrix Anal. Appl. 24, 603–626 (2003)MathSciNetCrossRef
8.
Bai, Z.Z., Benzi, M., Chen, F.: Modified HSS iteration methods for a class of complex symmetric linear systems. Computing 87, 93–111 (2010)MathSciNetCrossRef
9.
Bai, Z.Z., Benzi, M., Chen, F.: On preconditioned MHSS iteration methods for complex symmetric linear systems. Numer. Algor. 56, 297–317 (2011)MathSciNetCrossRef
10.
Hezari, D., Salkuyeh, D.K., Edalatpour, V.: A new iterative method for solving a class of complex symmetric system of linear equations. Numer. Algor. 73, 927–955 (2016)MathSciNetCrossRef
11.
Wang, T., Zheng, Q.Q., Lu, L.Z.: A new iteration method for a class of complex symmetric linear systems. J. Comput. Appl. Math. 325, 188–197 (2017)MathSciNetCrossRef
12.
Xiao, X.Y., Yin, H.W.: Efficient parameterized HSS iteration methods for complex symmetric linear systems. Comput. Math. Appl. 73, 87–95 (2017)MathSciNetCrossRef
13.
Huang, Z.G., Wang, L.G., Xu, Z., Cui, J.J.: An efficient two-step iterative method for solving a class of complex symmetric linear systems. Comput. Math. Appl. 75, 2473–2498 (2018)MathSciNetCrossRef
14.
Li, C.L., Ma, C.F.: On Euler-extrapolated Hermitian/skew-Hermitian splitting method for complex symmetric linear systems. Appl. Math. Lett. 86, 42–48 (2018)MathSciNetCrossRef
15.
Xiao, X.Y., Wang, X.: A new single-step iteration method for solving complex symmetric linear systems. Numer. Algor. 78, 643–660 (2018)MathSciNetCrossRef
16.
Zheng, Z., Huang, F.L., Peng, Y.C.: Double-step scale splitting iteration method for a class of complex symmetric linear systems. Appl. Math. Lett. 73, 91–97 (2017)MathSciNetCrossRef
17.
Bai, Z.Z., Guo, X.P.: On Newton-HSS methods for system of nonlinear equation with positive-definite Jacobian matrices. J. Comput. Math. 28, 235–260 (2010)MathSciNetCrossRef
18.
Guo, X.P., Duff, I.S.: Semilocal and global convergence of the Newton-HSS method for systems of nonlinear equations. Numer. Linear Algebra Appl. 18, 299–315 (2011)MathSciNetCrossRef
19.
Wu, Q.B., Chen, M.H.: Convergence analysis of modified Newton-HSS method for solving systems of nonlinear equations. Numer. Algor. 64, 659–683 (2013)MathSciNetCrossRef
20.
Chen, M.H., Lin, R.F., Wu, Q.B.: Convergence analysis of the modified Newton-HSS method under the Hölder continuous condition. J. Comput. Appl. Math. 264, 115–130 (2014)MathSciNetCrossRef
21.
Li, Y., Guo, X.P.: Multi-step modified Newton-HSS methods for systems of nonlinear equations with positive definite Jacobian matrices. Numer. Algor. 75, 55–80 (2017)MathSciNetCrossRef
22.
Wang, J., Guo, X.P., Zhong, H.X.: MN-DPMHSS iteration method for systems of nonlinear equations with block two-by-two complex Jacobian matrices. Numer. Algor. 77, 167–184 (2018)MathSciNetCrossRef
23.
Dai, P.F., Wu, Q.B., Chen, M.H.: Modified Newton-NSS method for solving systems of nonlinear equations. Numer. Algor. 77, 1–21 (2018)MathSciNetCrossRef
24.
Li, Y.M., Guo, X.P.: On the accelerated modified Newton-HSS method for systems of nonlinear equations. Numer. Algor. 79, 1049–1073 (2018)MathSciNetCrossRef
25.
Chen, M.H., Wu, Q.B.: Modified Newton-MDPMHSS method for solving nonlinear systems with block two-by-two complex symmetric Jacobian matrices. Numer. Algor. 80, 355–375 (2019)MathSciNetCrossRef
26.
27.
Yang, A.L., Wu, Y.J.: Newton-MHSS methods for solving systems of nonlinear equations with complex symmetric Jacobian matrices. Numer. Algebra, Control Optim. 2, 839–853 (2012)MathSciNetCrossRef
28.
Zhong, H.X., Chen, G.L., Guo, X.P.: On preconditioned modified Newton-MHSS method for systems of nonlinear equations with complex symmetric Jacobian matrices. Numer. Algor. 69, 553–567 (2015)MathSciNetCrossRef
Metadaten
Titel
Modified Newton-DSS method for solving a class of systems of nonlinear equations with complex symmetric Jacobian matrices
verfasst von
Fang Xie
Rong-Fei Lin
Qing-Biao Wu
Publikationsdatum
17.12.2019
Verlag
Springer US
Erschienen in
Numerical Algorithms / Ausgabe 3/2020
Print ISSN: 1017-1398
Elektronische ISSN: 1572-9265
DOI
https://doi.org/10.1007/s11075-019-00847-y

Weitere Artikel der Ausgabe 3/2020

Numerical Algorithms 3/2020 Zur Ausgabe

Original Paper

Transfinite mean value interpolation over polygons

Original Paper

Numerical methods based on the Floater–Hormann interpolants for stiff VIEs

Original Paper

Existence and approximation of fixed points of multivalued generalized α-nonexpansive mappings in Banach spaces

Original Paper

A note on generalized averaged Gaussian formulas for a class of weight functions

Original Paper

Iterative filtering as a direct method for the decomposition of nonstationary signals

Original Paper

Descent Perry conjugate gradient methods for systems of monotone nonlinear equations

Premium Partner

    Bildnachweise