Collocation Approximation to Eigenvalues of an Ordinary Differential Equation: The Principle of the Thing.

Abstract

It is shown that simple eigenvalues of an m-th order ordinary differential equation are approximated within 0(absolute value of delta to the 2k power) by collocation at Gauss points with piecewise polynomial functions of degree is less than m plus k on a mesh delta. The same rate is achieved by certain averages in case the eigenvalue is not simple. The argument relies on an extension and simplification of Osborn's recent results concerning the approximation of eigenvalues of compact linear maps.

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1979
Accession Number
ADA070197

Entities

People

  • Blair Swartz
  • Carl R. de Boor

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Air Platforms
  • Energy and Power Technologies
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Banach Space
  • Boundary Value Problems
  • Convergence
  • Differential Equations
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Errors
  • Mathematics
  • Military Research
  • North Carolina
  • Polynomials
  • Sequences
  • United States
  • Wisconsin

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Linear Algebra