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.
Descriptors:
Subject Categories:
- Numerical Mathematics