Accession Number : AD0747540

Title :   Stability Properties of Trigonometric Interpolating Operators,

Corporate Author : TEXAS UNIV AUSTIN CENTER FOR NUMERICAL ANALYSIS

Personal Author(s) : Morris,P. D. ; Cheney,E. W.

Report Date : AUG 1972

Pagination or Media Count : 21

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)

Descriptors :   (*INTERPOLATION, OPERATORS(MATHEMATICS)), POLYNOMIALS, FOURIER ANALYSIS, SERIES(MATHEMATICS), MAPPING(TRANSFORMATIONS), SET THEORY, THEOREMS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE