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Mathematics of Computation

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Minimax approximations subject to a constraint

Authors: C. T. Fike and P. H. Sterbenz
Journal: Math. Comp. 25 (1971), 295-298
MSC: Primary 41A20
MathSciNet review: 0303176
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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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Keywords: Rational approximation, polynomial approximation, best approximation, constrained approximation, exponential function, starting approximation for square root
Article copyright: © Copyright 1971 American Mathematical Society