Two Results on Polynomial Interpolation in Equally Spaced Points
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چکیده
We present two results that quantify the poor behavior of polynomial interpolation in n equally spaced points. First, in band-limited interpolation of complex exponential functions e‘li (c( E Iw), the error decreases to 0 as n + a, if and only if d( is small enough to provide at least six points per wavelength. Second, the Lebesgue constant ,4. (supremum norm of the nth interpolation operator) satisfies lim, j cc A,!,“‘= 2. Both of these results are more than 50 years old, but they are generally unknown to approximation theorists.
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تاریخ انتشار 1991