Accession Number:

ADA281638

Title:

On the Gibbs Phenomenon IV: Recovering Exponential Accuracy in a Sub- Interval From a Gegenbauer Partial Sum of a Piecewise Analytic Function

Descriptive Note:

Contractor rept.

Corporate Author:

INSTITUTE FOR COMPUTER APPLICATIONS IN SCIENCE AND ENGINEERING HAMPTON VA

Personal Author(s):

Report Date:

1994-05-01

Pagination or Media Count:

19.0

Abstract:

We continue our investigation of overcoming Gibbs phenomenon, i.e., to obtain exponential accuracy at all points including at the discontinuities themselves, from the knowledge of a spectral partial sum of a discontinuous but piecewise analytic function. We show that if we are given the first N Gegenbauer expansion coefficients, based on the Gegenbauer polynomials with the weight function of an L function fx, we can construct an exponentially convergent approximation to the point values of fx in any sub-interval in which the function is analytic. The proof covers the cases of Chebyshev or Legendre partial sums, which are most common in applications.

Subject Categories:

  • Numerical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE