Singular integral transforms and fast numerical algorithms
type: Item
instance of: scholarly article
title: Singular integral transforms and fast numerical algorithms
zbMATH Open document ID: 0916.65127
DOI: 10.1023/A:1019117414918
published in: Numerical Algorithms
publication date: 1999-07-19T00:00:00Z
review text: Fast algorithms for the evaluation of the singular integral transforms \[ T_mh(\sigma)= -{1\over\pi} \int \int_{B(0,1)} {h(\zeta)\over(\zeta- \sigma)^m} d\xi d\eta, \] \(\zeta= \xi+ i\eta\), where \(m= 1,2,\dots\), a complex-valued function \(h\) defiend on \(B(0,1)= \{z:| z|< 1\}\), are presented. They are based on some recursive relations in Fourier space and fast Fourier transform and have theoretical computational complexity of the order \(O(\log N)\) per point, where \(N^2\) is the total number of grid points.
Mathematics Subject Classification ID: 65R10
Mathematics Subject Classification ID: 65E05
Mathematics Subject Classification ID: 44A20
Mathematics Subject Classification ID: 65Y20
zbMATH DE Number: 1241256
zbMATH Keywords: fast algorithms
zbMATH Keywords: singular integral transforms
zbMATH Keywords: fast Fourier transform
zbMATH Keywords: computational complexity
author: Prabir Daripa
author: D. S. Mashat
reviewed by: Ilia V. Boikov
MaRDI profile type: Publication
full work available at URL: a:1019117414918
OpenAlex ID: W2098204775
description: scientific article; zbMATH DE number 1241256