On the Convergence of Inexact Newton Methods

  • Reijer IdemaEmail author
  • Domenico Lahaye
  • Cornelis Vuik
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 103)


A solid understanding of convergence behaviour is essential to the design and analysis of iterative methods. In this paper we explore the convergence of inexact iterative methods in general, and inexact Newton methods in particular. A direct relationship between the convergence of inexact Newton methods and the forcing terms is presented in both theory and numerical experiments.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    R.S. Dembo, S.C. Eisenstat, T. Steihaug, Inexact Newton methods. SIAM J. Numer. Anal. 19(2), 400–408 (1982)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    J.E. Dennis Jr., R.B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations (SIAM, Philadelphia, 1996)CrossRefzbMATHGoogle Scholar
  3. 3.
    S.C. Eisenstat, H.F. Walker, Choosing the forcing terms in an inexact Newton method. SIAM J. Sci. Comput. 17(1), 16–32 (1996)CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    R. Idema, D.J.P. Lahaye, C. Vuik, L. van der Sluis, Scalable Newton-Krylov solver for very large power flow problems. IEEE Trans. Power Syst. 27(1), 390–396 (2012)CrossRefGoogle Scholar
  5. 5.
    R. Idema, G. Papaefthymiou, D.J.P. Lahaye, C. Vuik, L. van der Sluis, Towards faster solution of large power flow problems. IEEE Trans. Power Syst. 28(4), 4918–4925 (2013)CrossRefGoogle Scholar
  6. 6.
    J.M. Ortega, W.C. Rheinboldt, Iterative solution of nonlinear equations in several variables (SIAM, Philadelphia, 2000)CrossRefzbMATHGoogle Scholar
  7. 7.
    Y. Saad, M.H. Schultz, GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 7, 856–869 (1986)CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Delft Institute of Applied MathematicsDelft University of TechnologyDelftNetherlands

Personalised recommendations