ON THE APPROXIMATE SOLUTION OF FREDHOLM INTEGRAL EQUATIONS OF THE FIRST KIND

Abstract

The problem of obtaining good approximate solutions to u(t) = the integral over S of K(t,s) z(s)ds, t = t sub 1, t sub 2,..., t sub n, is discussed as a problem in the approximation of one continuous linear functional in a reproducing kernel Hilbert space, by several others. The methods of regularization and statistical estimation are shown to be special cases. Pointwise error bounds and a criteria for choosing the regularization parameter are given.

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1969
Accession Number
AD0703191

Entities

People

  • Grace Wahba

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Autonomy
  • Materials and Manufacturing Processes
  • Space

DTIC Thesaurus Topics

  • Air Force
  • Algorithms
  • Boundaries
  • Coefficients
  • Covariance
  • Equations
  • Geometry
  • Hilbert Space
  • Integral Equations
  • Mathematics
  • Numbers
  • Random Variables
  • Real Numbers
  • Statistical Estimation
  • Stochastic Processes
  • United States
  • Wisconsin

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis

Technology Areas

  • Space