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Exponential Chebyshev approximation on finite subsets of $ [0,\,1]$


Author: Bernard H. Rosman
Journal: Math. Comp. 25 (1971), 575-577
MSC: Primary 41A50; Secondary 65D15
DOI: https://doi.org/10.1090/S0025-5718-1971-0295533-5
MathSciNet review: 0295533
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Abstract: In this note the convergence of best exponential Chebyshev approximation on finite subsets of [0,1] to a best approximation on the interval is proved when the function to be approximated is continuous and when the union of the finite subsets is dense in [0, 1].


References [Enhancements On Off] (What's this?)

  • [1] T. J. Rivlin & E. W. Cheney, ``A comparison of uniform approximations on an interval and a finite subset thereof,'' SIAM J. Numer. Anal., v. 3, 1966, pp. 311-320. MR 34 #4773. MR 0204938 (34:4773)
  • [2] C. B. Dunham, ``Rational Chebyshev approximation on subsets,'' J. Approximation Theory, v. 1, 1968, pp. 484-487. MR 38 #6279. MR 0238002 (38:6279)
  • [3] J. R. Rice, The Approximation of Functions. Vol. 2: Nonlinear and Multivariate Theory, Addison-Wesley, Reading, Mass., 1969. MR 39 #5989. MR 0244675 (39:5989)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1971-0295533-5
Keywords: Chebyshev approximation, exponential functions, varisolvence, pointwise convergence, uniform convergence
Article copyright: © Copyright 1971 American Mathematical Society

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