Fast computation of contour integrals of rational functions
type: Item
instance of: scholarly article
title: Fast computation of contour integrals of rational functions
zbMATH Open document ID: 0948.65020
author: Peter Kirrinnis
published in: Journal of Complexity
publication date: 2000-06-22T00:00:00Z
review text: If polynomials \(q, p\in \mathbb{C}[z]\) and a complex curve \(\Gamma\) are given, the contour integral \(\int_\Gamma q(z)/p(z)dz\) is computed up to a prescribed error. The first step of this fast algorithm is a decomposition of \(q/p\) into partial fractions corresponding to well separated clusters of roots of \(p\), where the author's method [J. Complexity 14, No. 3, 378-444 (1998; Zbl 0934.12005)] is used. Then the integrals of the partial fractions are computed by integrating their Laurent series termwise. This algorithm is analyzed with respect to the bit complexity. The running time of the algorithm is also estimated.
reviewed by: Manfred Tasche
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 30E20
Mathematics Subject Classification ID: 68Q25
Mathematics Subject Classification ID: 65E05
Mathematics Subject Classification ID: 65Y20
Mathematics Subject Classification ID: 68W30
zbMATH DE Number: 1444124
zbMATH Keywords: contour integral
zbMATH Keywords: rational function
zbMATH Keywords: fast algorithm
zbMATH Keywords: clusters of roots
zbMATH Keywords: partial fraction decomposition
zbMATH Keywords: Laurent series
zbMATH Keywords: bit complexity
zbMATH Keywords: running time
zbMATH Keywords: algorithm
MaRDI profile type: Publication
OpenAlex ID: W1993200051
cites work: The Arithmetic-Geometric Mean and Fast Computation of Elementary Functions
cites work: Q3476890
cites work: Asymptotic behavior of automatic quadrature
cites work: Q4234216
cites work: Partial fraction decomposition in \(\mathbb{C}(z)\) and simultaneous Newton iteration for factorization in \(\mathbb{C}^{[z]}\)
cites work: Q3993279
DOI: 10.1006/JCOM.1999.0531
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description: scientific article; zbMATH DE number 1444124