Application of Orthogonalisation Procedures for Gaussian Radial Basis Functions and Chebyshev Polynomials

Abstract

Procedures for orthogonalisation of Gaussians and B-splines are recalled and it is shown that, provided Gaussians are negligible in appropriate regions, the same recurrence formulae may be adopted in both and render the computation relatively efficient. Chebyshev polynomial collocation is well known to be rapidly defined by discrete orthogonalisation, and similar ideas are commonly applicable to partial differential equations (PDEs) and integral equations (IEs). However, it is shown that the most elementary mixed methods (both boundary conditions and PDEs being satisfied) for the Dirichlet problem in rectangular types of domain can lead to a singular linear system, which may be rendered non-singular, for example, by a small modification of interpolation nodes.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Jul 01, 2001
Accession Number
ADP013733

Entities

People

  • Andrew S. Crampton
  • John C. Mason

Organizations

  • University of Huddersfield

Tags

DTIC Thesaurus Topics

  • Accuracy
  • Algorithms
  • Boundaries
  • Chebyshev Polynomials
  • Coefficients
  • Equations
  • Geometry
  • Identities
  • Intervals
  • Mathematics
  • Normal Distribution
  • Orthogonality
  • Oscilloscopes
  • Polynomials
  • Technical Information Centers
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)