On the Gibbs Phenomenon III: Recovering Exponential Accuracy in a Sub- Interval from a Spectral Partial Sum of a Piecewise Analytic Function
Abstract
We continue the investigation of overcoming Gibbs phenomenon, i.e., obtaining 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 expansion coefficients of an L2 function f(x) in terms of either the trigonometrical polynomials or the Chebyshev or Legendre polynomials, we can construct an exponentially convergent approximation to the point values of f(x) in any sub- interval in which it is analytic.
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 1993
- Accession Number
- ADA274823
Entities
People
- Chi-Wang Shu
- David Gottlieb