Approximate Integration Using Iterated Levin Transformation

Carino, R.L., DeDoncker, E., & Robinson, I. (1989). Approximate Integration Using Iterated Levin Transformation. In N.A. Sherwani et al (Eds.), Lecture Notes in Computer Science. Springer Verlag. 507, 293-299.

The efficiency of a quadrature scheme based on iterated Levin U transformations and composite rule approximations for a harmonic sequence of mesh ratios is demonstrated for typical problem classes. Numerical results indicate a favourable comparison with the well known nonlinear extrapolation procedures applied to a sequence of composite quadrature rule sums for a geometric progression of the mesh ratios.