On the Stability of Certain Interpolation Problems
نویسنده
چکیده
In this work we present a number of results concerning the nite dimensional band-limited interpolation problem. Our aim is to understand how the stability of the interpolation problem is aaected by changes in the positions of the interpolation knots. We give upper and lower bounds for the eigenvalues of the interpolation matrix, as functions of the gaps between missing samples. The upper bound is especially useful, since it determines the convergence rate of an iterative interpolation procedure, and the conditioning of an equivalent noniterative method. The interplay between convergence rate, stability, normalized band-width of the data, and minimum gap between missing samples is clariied.
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