On the Spline-Based Wavelet Differentiation Matrix

Abstract

The differentiation matrix for a spline-based wavelet basis will be constructed. Given an n-th order spline basis it will be proven that the differentiation matrix is accurate of order 2n + 2 when periodic boundary conditions are assumed. This high accuracy, or superconvergence, is lost when the boundary conditions are no longer periodic. Furthermore, it will be shown that spline-based bases generate a class of compact finite difference schemes. Differentiation matrix, Wavelets, Superconvergence.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1993
Accession Number
ADA274278

Entities

People

  • Leland Jameson

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Accuracy
  • Boundaries
  • Coefficients
  • Construction
  • Contracts
  • Convolution
  • Decomposition
  • Differential Equations
  • Discrete Fourier Transforms
  • Equations
  • Errors
  • Frequency
  • Integrals
  • Intervals
  • Partial Differential Equations
  • Personality
  • Sequences

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Image Processing and Computer Vision.