4 papers · 1 filter
An adaptive delaminating Levin method in two dimensions
Shukui Chen, Kirill Serkh, James Bremer +1
We present an adaptive delaminating Levin method for evaluating bivariate oscillatory integrals over rectangular domains. Whereas previous analyses of Levin methods impose non-reso…
On polynomial interpolation in the monomial basis
Zewen Shen, Kirill Serkh
In this paper, we show that the monomial basis is generally as good as a well-conditioned polynomial basis for interpolation, provided that the condition number of the Vandermonde…
On the Approximation of Singular Functions by Series of Non-integer Powers
Mohan Zhao, Kirill Serkh
In this paper, we describe an algorithm for approximating functions of the form over , where is some signed Radon measure, o…
An adaptive Levin method for complicated domains
Shukui Chen, Kirill Serkh, James Bremer
In this paper we describe an adaptive Levin method for numerically evaluating integrals of the form over general domains that have…