Iterative Methods for Best Approximate Solutions of Linear Integral Equations of the First and Second Kinds

Abstract

Least squares solutions of Fredholm and Volterra equations of the first and second kinds are studied using generalized inverses. The method of successive approximations, the steepest descent and the conjugate gradient methods are shown to converge to a least squares solution or to a least squares solution of minimal norm, both for integral equations of the first and second kinds. An iterative method for matrices due to Cimmino is generalized to integral equations of the first kind and its convergence to the least squares solution of minimal norm is established.

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1971
Accession Number
AD0735836

Entities

People

  • M. Z. Nashed
  • W. J. Kammerer

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Applied Mathematics
  • Banach Space
  • Bibliographies
  • Convergence
  • Differential Equations
  • Eigenvalues
  • Equations
  • Formulas (Mathematics)
  • Functional Analysis
  • Hilbert Space
  • Integral Equations
  • Mathematics
  • New York
  • Numerical Analysis
  • United States
  • Volterra Equations

Fields of Study

  • Mathematics

Readers

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