A posteriori component-wise error estimation of approximate solutions to nonlinear equations

  • Minoru Urabe
Part of the Lecture Notes in Computer Science book series (LNCS, volume 29)


In the present paper, extending Proposition 2 of [2] by the use of the techniques developed in [4], the author establishes a theorem which gives a method of a posteriori component-wise error estimation for approximate solutions to nonlinear equations. The method of error estimation based on this theorem is illustrated with a system consisting of two nonlinear equations.


Approximate Solution Nonlinear Equation Posteriori Error Fundamental Theorem Posteriori Error Estimate 
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  1. [1]
    Kantorovich, L. V. and G. P. Akilov: Functional Analysis in Normed Spaces, Translated from the Russian by D. E. Brown, M. A., Pergamon Press, Oxford, 1964, p. 708–711.Google Scholar
  2. [2]
    Urabe, M.: Galerkin's procedure for nonlinear periodic systems, Arch. Rational Mech. Anal., 20 (1965), 120–152.CrossRefGoogle Scholar
  3. [3]
    —: Numerical solution of multi-point boundary value problems in Chebyshev series — Theory of the method, Numer. Math., 9 (1967), 341–366.Google Scholar
  4. [4]
    —: Component-wise error analysis of iterative methods practiced on a floating-point system, Mem. Fac. Sci., Kyushu Univ., Ser. A, Math., 27 (1973), 23–64.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1975

Authors and Affiliations

  • Minoru Urabe
    • 1
  1. 1.Department of Mathematics, Faculty of ScienceKyushu UniversityFukuokaJapan

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