Double Exponential Formulas for Numerical Integration
- 31 December 1973
- journal article
- Published by European Mathematical Society - EMS - Publishing House GmbH in Publications of the Research Institute for Mathematical Sciences
- Vol. 9 (3) , 721-741
- https://doi.org/10.2977/prims/1195192451
Abstract
A family of numerical quadrature formulas is introduced by application of the trapezoidal rule to infinite integrals which result from the given integrals \int^b_a f(x)dx by suitable variable transformations x = \phi(u) . These formulas are characterized by having double exponential asymptotic behavior of the integrands in the resulting infinite integrals as u →± ∞ , and it is shown both analytically and numerically that such formulas are generally optimal with respect to the ecomony of the number of sampling points.This publication has 0 references indexed in Scilit: