# Simultaneous Interpolation and Approximation

• R. Gervais
• Q. I. Rahman
• G. Schmeisser
Part of the NATO Advanced Study Institutes Series book series (ASIC, volume 49)

## Abstract

Given the values of a function and possibly the values of some of its derivatives, at certain points, a practical problem of numerical analysis is to use this information to construct other functions which approximate it. Simultaneous interpolation and approximation of continuous functions on a compact interval, by polynomials, has been extensively studied by Runge, Bernstein, Faber, Fejer, Turan and others. Here we study simultaneous interpolation and approximation of a function f on the whole real line by entire functions of exponential type. The function f is supposed to be uniformly continuous and bounded on (-∞,∞).

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