Chebyshev Approximation by A + B* log (1 + CX). II
- 1 December 1972
- journal article
- research article
- Published by Oxford University Press (OUP) in IMA Journal of Applied Mathematics
- Vol. 10 (3) , 369-372
- https://doi.org/10.1093/imamat/10.3.369
Abstract
The set of all first degree polynomials must be added to the set of approximations of the form a + b log (1 + cx) in order that a best Chebyshev approximation exist to all continuous functions on [0, α]. Best approximations in this augmented family of approximations are characterized by alternation of their error curve and are unique. The Chebyshev operator is continuous at f if f is an approximant or f has a non-constant best approximation.Keywords
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