The Mathematical Institute, University of Oxford, Eprints Archive

Chebyshev interpolation for functions with endpoint singularities via exponential and double-exponential transforms

Richardson, Mark (2012) Chebyshev interpolation for functions with endpoint singularities via exponential and double-exponential transforms. Technical Report. SINUM. (Submitted)

[img]
Preview
PDF
636Kb

Abstract

We present five theorems concerning the asymptotic convergence rates of Chebyshev interpolation applied to functions transplanted to either a semi-infinite or an infinite interval under exponential or double-exponential transformations. This strategy is useful for approximating and computing with functions that are analytic apart from endpoint singularities. The use of Chebyshev polynomials instead of the more commonly used cardinal sinc or Fourier interpolants is important because it enables one to apply maps to semi-infinite intervals for functions which have only a single endpoint singularity. In such cases, this leads to significantly improved convergence rates.

Item Type:Technical Report (Technical Report)
Subjects:A - C > Approximations and expansions
H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1497
Deposited By:Lotti Ekert
Deposited On:06 Mar 2012 07:37
Last Modified:07 Mar 2012 11:34

Repository Staff Only: item control page