Accession Number : AD0642920

Title :   ON VARIATION DIMINISHING SPLINE APPROXIMATION METHODS.

Descriptive Note : Technical summary rept.,

Corporate Author : WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : Marsden,Martin ; Schoenberg,I. J.

Report Date : JUN 1966

Pagination or Media Count : 33

Abstract : 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)

Descriptors :   (*APPROXIMATION(MATHEMATICS), *FUNCTIONS(MATHEMATICS)), ERRORS, IDENTITIES, POLYNOMIALS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE