# 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

# Descriptors:

# Subject Categories:

- Theoretical Mathematics