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1. An IMT-type quadrature formula with the same asymptotic performance as the DE formula

Author

Takuya Ooura

Subjects
Numerical quadrature, DE formula, Applied Mathematics, Double exponential formula, Gauss–Laguerre quadrature, Euler–Maclaurin formula, IMT-type quadrature, Gauss–Kronrod quadrature formula, Tanh-sinh quadrature, Computational Mathematics, symbols.namesake, Calculus, symbols, Gauss–Jacobi quadrature, Applied mathematics, Asymptotic formula, Gauss–Hermite quadrature, Mathematics, Clenshaw–Curtis quadrature
Abstract

We propose an IMT-type quadrature formula which achieves the same asymptotic error estimate as the DE formula. The point of the idea is to optimize the parameters of the IMT-type transformation depending on the number of sampling points. We also show the performance of our IMT-type quadrature formula by numerical examples.

Published
2008
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