Abstract
In practical computation of the discrete best uniform approximation, we usually only get “near best” (i.e., with the “ε-near alteration property”) approximation. We need to estimate the error between the (unknown) best approximation and the achieved approximation. In this paper we estimate the parameter error by means of the generalized strong unicity constants.
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References
E. Cheney,Introduction to Approximation Theory, McGraw-Hill, 1966.
C. Dunham,Discrete Chebyshev approximation: Alternation and the Remez algorithm, ZAMM 58 (1979), pp. 326–328.
C. Dunham,Uniform local strong uniqueness on finite subsets, Aequationes Math., to appear.
C. Dunham and C. Zhu,Computation of the modified strong uniqueness constants, Intern. J. Computer Math., 52 (1994), pp. 83–97.
C. Dunham and C. Zhu,Application of modified local strong uniqueness constant to exponential approximation, Technical Report No. 381, Department of Computer Science, The University of Western Ontario, August, 1993.
G. Meinardus,Approximation of Functions, Springer-Verlag, New York, 1967.
J. Rice,The Approximation of Functions, Vol. 1, Addison-Wesley, Reading, Mass., 1964.
D. Schmidt, C. Zhu and C. Dunham,Generalized strong uniqueness constant in linear uniform approximation, in preparation.
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Visiting scholar from Department of Mathematics, Shanghai University of Science and Technology, Shanghai, P.R. China 201800.
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Zhu, C.Z., Dunham, C.B. Parameter error estimate of near alternation approximation. Bit Numer Math 35, 133–142 (1995). https://doi.org/10.1007/BF01732982
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DOI: https://doi.org/10.1007/BF01732982