Fast non-polynomial interpolation and integration for functions with logarithmic singularities
Numerical Analysis
2018-05-08 v1
Abstract
A fast non-polynomial interpolation is proposed in this paper for functions with logarithmic singularities. It can be executed fast with the discrete cosine transform. Based on this interpolation, a new quadrature is proposed for a kind of logarithmically singular integrals. The interpolation and integration errors are also analyzed. Numerical examples of the interpolation and integration are shown to validate the efficiency of the proposed new interpolation and the new quadrature.
Cite
@article{arxiv.1805.02088,
title = {Fast non-polynomial interpolation and integration for functions with logarithmic singularities},
author = {Yinkun Wang and Xiangling Chen and Ying Li and Jianshu Luo},
journal= {arXiv preprint arXiv:1805.02088},
year = {2018}
}
Comments
13 pages, 2 figures, 8 tables, accepted by Journal of Computational and Applied Mathematics