Abstract:A class of approximation problems is considered in which a continuous, positive function $\varphi (x)$ is approximated by a rational function satisfying some identity. It is proved under certain hypotheses that there is a unique rational approximation satisfying the constraint and yielding minimax relative error and that the corresponding relative-error function does not have an equal-ripple graph. This approximation is, moreover, just the rational approximation to $\varphi (x)$ yielding minimax logarithmic error. This approximation, in turn, is just a constant multiple of the rational approximation to $\varphi (x)$ yielding minimax relative error but not necessarily satisfying the constraint.
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- © Copyright 1971 American Mathematical Society
- Journal: Math. Comp. 25 (1971), 295-298
- MSC: Primary 41A20
- DOI: https://doi.org/10.1090/S0025-5718-1971-0303176-X
- MathSciNet review: 0303176