ON VARIATION DIMINISHING SPLINE APPROXIMATION METHODS.
Technical summary rept.,
WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
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In Technical Summary Report 625 AD-638 656 Schoenberg introduced a certain class of variation diminishing spline approximations which included as special cases the linear interpolation methods as well as the Bernstein polynomials. Concerning error bounds a few results were there only stated without proofs. Using a new identity for spline functions due to M. Marsden, the authors discuss here the question of convergence and also the closeness of individual approximations. The main result is that the spline approximations of low degree cubic, for instance have all the virtues of the linear interpolation method, while providing approximations having any desired number of continuous derivatives. Author
- Theoretical Mathematics