Wavelets for the Fast Solution of Second-Kind Integral Equations

Abstract

A class of vector-space bases is introduced for the sparse representation of discretizations of integral operators. An operator with a smooth, non-oscillatory kernel possessing a finite number of singularities in each row or column is represented in these bases as a sparse matrix, to high precision. A method is presented that employs these bases for the numerical solution of second-kind integral equations in time bounded by O(nlog squared n) , where n is the number of points in the discretization. Numerical results are given which demonstrate the effectiveness of the approach, and several generalizations and applications of the method are discussed.

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1990
Accession Number
ADA233650

Entities

People

  • B. Alpert
  • G. Beylkin
  • R. Coifman
  • Vladimir Rokhlin

Organizations

  • Yale University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Accuracy
  • Algorithms
  • Analytic Functions
  • Bandwidth
  • Coefficients
  • Computations
  • Construction
  • Data Analysis
  • Differential Equations
  • Equations
  • Integral Equations
  • Integrals
  • Partial Differential Equations
  • Polynomials
  • Precision
  • Sparse Matrix
  • Vector Spaces

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Linear Algebra

Technology Areas

  • Space