Accession Number:

AD0747540

Title:

Stability Properties of Trigonometric Interpolating Operators,

Descriptive Note:

Corporate Author:

TEXAS UNIV AUSTIN CENTER FOR NUMERICAL ANALYSIS

Personal Author(s):

Report Date:

1972-08-01

Pagination or Media Count:

21.0

Abstract:

The interpolating operator P studied here is the one which produces a trigonometric polynomial of order n taking prescribed values at 2n 1 equally-spaced nodes theta sub j 2 pi j 2n 1, j 0,...,2n. This operator P acts in the space C of 2 pi-periodic continuous real functions, normed with the supremum norm. For any point, phi, other than a node, there is a 2n 1-dimensional manifold of projections carried by the point set theta sub o,...,theta sub 2n, phi. The first theorem states that P is the element of least norm in this manifold. Another theorem asserts that if 3 correctly-chosen points are adjoined to the set of nodes, then P is no longer a minimal element in the manifold of projections carried by that point set. Various other related results are given. Author

Subject Categories:

  • Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE