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):

Report Date:

1973-04-01

Pagination or Media Count:

12.0

Abstract:

In previous papers special classes of functions fx, defined for all real x, were established with the property that if S sub mx is the unique cardinal spline interpolant of fx, of degree 2m-1, then S sub mx converges to fx, 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

Subject Categories:

  • Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE