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Existence questions for the problem of Chebyshev approximation by interpolating rationals


Authors: G. D. Taylor and J. Williams
Journal: Math. Comp. 28 (1974), 1097-1103
MSC: Primary 41A50
DOI: https://doi.org/10.1090/S0025-5718-1974-0355435-5
MathSciNet review: 0355435
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Abstract: This paper considers a problem of Chebyshev approximation by interpolating rationals. Examples are given which show that best approximations may not exist. Sufficient conditions for existence are established, some of which can easily be checked in practice. Illustrative examples are also presented.


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DOI: https://doi.org/10.1090/S0025-5718-1974-0355435-5
Keywords: Existence of best rational interpolants, Chebyshev approximation, uniform rational approximation with interpolatory constraints
Article copyright: © Copyright 1974 American Mathematical Society