Accession Number:

ADA275526

Title:

On the Daubechies-Based Wavelet Differentiation Matrix

Descriptive Note:

Contractor's rept.

Corporate Author:

INSTITUTE FOR COMPUTER APPLICATIONS IN SCIENCE AND ENGINEERING HAMPTON VA

Personal Author(s):

Report Date:

1993-12-01

Pagination or Media Count:

54.0

Abstract:

The differentiation matrix for a Daubechies-based wavelet basis will be constructed and superconvergence will be proven. That is, it will be proven that under the assumption of periodic boundary conditions that the differentiation matrix is accurate of order 2M, even though the approximation subspace can represent exactly only polynomials up to degree M - 1, where M is the number of vanishing moments of the associated wavelet. It will be illustrated that Daubechies-based wavelet methods are equivalent to finite difference methods with grid refinement in regions of the domain where small- scale structure is present.

Subject Categories:

  • Numerical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE