Accession Number : AD0761869

Title :   Notes on Spline Functions, III: On the Convergence of the Interpolating Cardinal Splines as Their Degree Tends to Infinity.

Descriptive Note : Technical summary rept.,

Corporate Author : WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : Schoenberg,I. J.

Report Date : APR 1973

Pagination or Media Count : 12

Abstract : In previous papers special classes of functions f(x), defined for all real x, were established with the property that if (S sub m)(x) is the unique cardinal spline interpolant of f(x), of degree 2m-1, then (S sub m)(x) converges to f(x), uniformally for all real x. Reporting about these results in a monograph, the author raised the question of the existence of a comprehensive theory that would contain these separate results as special cases. Such a theory is developed in the present note. It is based on the properties of the so-called exponential Euler spline and the proof of the more general result is far simpler than the proofs given earlier for the special cases. (Modified author abstract)

Descriptors :   (*INTERPOLATION, FUNCTIONS(MATHEMATICS)), POLYNOMIALS, INEQUALITIES, CONVERGENCE, THEOREMS, INTEGRAL TRANSFORMS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE