Abstract
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.
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References
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.
Urabe, M.: Galerkin's procedure for nonlinear periodic systems, Arch. Rational Mech. Anal., 20 (1965), 120–152.
—: Numerical solution of multi-point boundary value problems in Chebyshev series — Theory of the method, Numer. Math., 9 (1967), 341–366.
—: 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.
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© 1975 Springer-Verlag Berlin Heidelberg
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Urabe, M. (1975). A posteriori component-wise error estimation of approximate solutions to nonlinear equations. In: Nickel, K. (eds) Interval Mathematics. IMath 1975. Lecture Notes in Computer Science, vol 29. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-07170-9_7
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DOI: https://doi.org/10.1007/3-540-07170-9_7
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