A Smooth and Local Interpolant with 'Small' k-th Derivative.
WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
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This report is a continuation of MRC TSR 1425, How small can one make the derivatives of an interpolating function., and is concerned with estimating the number K sub 0 inf C sub k with the infimum taken over all C sub k. Knowledge about K sub 0k makes it possible to estimate the derivatives up to and including the k-th of some smooth interpolant to give data directly from the divided differences of the data without actually constructing such an interpolant and its derivatives, thus facilitating the process of estimating the residual error of a finite difference approximation.
- Theoretical Mathematics