Application and Numerical Solution of Abel-Type Integral Equations.

Abstract

This paper reviews the numerous applications in which the solution of equations like the Abel-type integral equation for discrete observational data (d sub i) is the basic step, compares, with respect to given discrete observational data (d sub i), the use of pseudo-analytic methods and the direct evaluation of its inversion formulas as a basis for solving this equation, proposes a specific algorithm based on these conclusions, and examines the consequences of the fact that, for the equation, linear functionals defined on its solution u(x) can be redefined as linear functionals on the data s(y). The justification for the latter is that, in applications involving separable first kind Abel-type integral equations, inferences are usually based on (linear) functionals defined on u(x), not on u(x) itself. This point is illustrated with an example from metallurgy.

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1977
Accession Number
ADA049396

Entities

People

  • R. S. Anderssen

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Air Platforms
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Brownian Motion
  • Computational Science
  • Equations
  • Estimators
  • Geometry
  • Integral Equations
  • Integrals
  • Mathematical Analysis
  • Mathematics
  • Metallurgy
  • Microscopy
  • Numerical Analysis
  • Particle Size
  • Statistics
  • Three Dimensional
  • United States

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Combustion Dynamics and Shock Wave Physics.
  • Operations Research

Technology Areas

  • AI & ML
  • AI & ML - Bayesian Inference
  • AI & ML - Machine Learning Algorithms