Trefethen, Lloyd N. (2006) Is Gauss quadrature better than ClenshawCurtis? Technical Report. Unspecified. (Submitted)

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Abstract
We consider the question of whether Gauss quadrature, which is very famous, is more powerful than the much simpler ClenshawCurtis quadrature, which is less wellknown. Sevenline MATLAB codes are presented that implement both methods, and experiments show that the supposed factorof2 advantage of Gauss quadrature is rarely realized. Theorems are given to explain this effect. First, following Elliott and O'Hara and Smith in the 1960s, the phenomenon is explained as a consequence of aliasing of coefficients in Chebyshev expansions. Then another explanation is offered based on the interpretation of a quadrature formula as a rational approximation of in the complex plane. Gauss quadrature corresponds to Pade approximation at . ClenshawCurtis quadrature corresponds to an approximation whose order of accuracy at is only half as high, but which is nevertheless equally accurate near .
Item Type:  Technical Report (Technical Report) 

Subjects:  A  C > Approximations and expansions H  N > Numerical analysis 
Research Groups:  Numerical Analysis Group 
ID Code:  1116 
Deposited By:  Lotti Ekert 
Deposited On:  11 May 2011 09:56 
Last Modified:  29 May 2015 18:48 
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