3 papers
math.NA2025
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…
math.NA2025
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…
math.NA2024
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…