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New quadrature formulas from conformal maps

Abstract:

Gauss and Clenshaw-Curtis quadrature, like Legendre and Chebyshev spectral methods, make use of grids strongly clustered at boundaries. From the viewpoint of polynomial approximation this seems necessary and indeed in certain respects optimal. Nevertheless such methods may "waste" a factor of π/2 with respect to each space dimension. We propose new non-polynomial quadrature methods that avoid this effect by conformally mapping the usual ellipse of convergence to an infinite strip or another a...

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Publisher:
Unspecified
Publication date:
2007-06-01
UUID:
uuid:d3df5fee-4416-41bb-9e40-c59ddb43eb4b
Local pid:
oai:eprints.maths.ox.ac.uk:1087
Deposit date:
2013-09-17

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