The Mathematical Institute, University of Oxford, Eprints Archive

The exponentially convergent trapezoidal rule

Trefethen, Lloyd N. and Weideman, J. A. C. (2013) The exponentially convergent trapezoidal rule. Technical Report. SIAM. (Submitted)

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Abstract

It is well known that the trapezoidal rule converges geometrically when applied to analytic functions on periodic intervals or the real line. The mathematics and history of this phenomenon are reviewed and it is shown that far from being a curiosity, it is linked with computational methods all across scientific computing, including algorithms related to inverse Laplace transforms, special functions, complex analysis, rational approximation, integral equations, and the computation of functions and eigenvalues of matrices and operators.

Item Type:Technical Report (Technical Report)
Subjects:D - G > Fourier analysis
H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1734
Deposited By: Lotti Ekert
Deposited On:08 Aug 2013 07:41
Last Modified:29 May 2015 19:25

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