Application of Orthogonalisation Procedures for Gaussian Radial Basis Functions and Chebyshev Polynomials
HUDDERSFIELD UNIV (UNITED KINGDOM) SCHOOL OF COMPUTING AND MATHEMATICS
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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.
- Numerical Mathematics
- Theoretical Mathematics