On the Gibbs Phenomenon IV: Recovering Exponential Accuracy in a Sub- Interval From a Gegenbauer Partial Sum of a Piecewise Analytic Function
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 f(x), we can construct an exponentially convergent approximation to the point values of f(x) 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.
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1994
- Accession Number
- ADA281638
Entities
People
- Chi-Wang Shu
- David Gottlieb