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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
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].

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  • [1] T. J. Rivlin and E. W. Cheney, A comparison of uniform approximations on an interval and a finite subset thereof, SIAM J. Numer. Anal. 3 (1966), 311–320. MR 0204938
  • [2] Charles B. Dunham, Rational Chebyshev approximation on subsets, J. Approximation Theory 1 (1968), 484–487. MR 0238002
  • [3] John R. Rice, The approximation of functions. Vol. 2: Nonlinear and multivariate theory, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1969. MR 0244675

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Keywords: Chebyshev approximation, exponential functions, varisolvence, pointwise convergence, uniform convergence
Article copyright: © Copyright 1971 American Mathematical Society