Minimax separation of the Cauchy kernel

We prove and apply an optimal low-rank approximation of the Cauchy kernel over separated real domains. A skeleton decomposition is the minimum over real-valued functions of the maximum relative pointwise error. We present an algorithm to optimize its parameters, demonstrate suboptimal but effective...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2020-10
Main Author: Moussa, Jonathan E
Format: Article
Language:English
Subjects:
Decomposition
Domains
Kernels
Mathematical analysis
Mathematical functions
Minimax technique
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We prove and apply an optimal low-rank approximation of the Cauchy kernel over separated real domains. A skeleton decomposition is the minimum over real-valued functions of the maximum relative pointwise error. We present an algorithm to optimize its parameters, demonstrate suboptimal but effective heuristic approximations, and identify numerically stable forms.
ISSN:2331-8422