A Wavelet-Based Preconditioning Method for Dense Matrices with Block Structure

Abstract

In recent years application of a discrete wavelet transform (DWT) has become an established tool for the design of preconditioners for smooth, dense matrices, such as those that arise in the solution of certain integral equations. In this paper we consider the higher dimensional case, where the matrix A is not itself smooth, but has a smooth block structure. To precondition such matrices, we use repeated application of a level 1 block-wise DWT to exploit the fact that corresponding entries in adjacent blocks are close in value. We illustrate the effectiveness of our methods by means of numerical examples.

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 2001
Accession Number
ADP013746

Entities

People

  • Judith M. Ford
  • Ke Chen

Organizations

  • University of Liverpool

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Compression
  • Computational Fluid Dynamics
  • Engineering
  • Equations
  • High Pass Filters
  • Iterations
  • Linear Systems
  • Physical Sciences
  • Standards
  • Technical Information Centers
  • Two Dimensional
  • Unmanned Ground Systems
  • Wavelet Transforms

Fields of Study

  • Engineering
  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Image Processing and Computer Vision.
  • Linear Algebra