On the calculation of the poles of multivariate meromorphic functions using the symbolic-numeric two-point qd-algorithm

The so-called quotient-difference algorithm, or qd-algorithm, is used for determining the poles of a meromorphic function from its Taylor coefficients. A generalization of this algorithm to the univariate and multivariate two-point cases applied to a power series (positive or negative exponents) is...

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Bibliographic Details
Published in:Numerical algorithms Vol. 84; no. 4; pp. 1443 - 1458
Main Authors: Elidrissi, A., Abouir, J., Benouahmane, B.
Format: Journal Article
Language:English
Published: New York Springer US 01.08.2020
Springer Nature B.V
Subjects:
Algebra
Algorithms
Computer Science
Eigenvalues
Meromorphic functions
Multivariate analysis
Numeric Computing
Numerical Analysis
Original Paper
Poles
Polynomials
Power series
Series expansion
Theory of Computation
Thermal expansion
Poles
Multivariate approximation
41A20
Series expansions
41A21
Two-point Padé approximants
Eigenvalues
65D15
qd-algorithm
ISSN:1017-1398, 1572-9265
Online Access:Get full text
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Summary:The so-called quotient-difference algorithm, or qd-algorithm, is used for determining the poles of a meromorphic function from its Taylor coefficients. A generalization of this algorithm to the univariate and multivariate two-point cases applied to a power series (positive or negative exponents) is presented. We describe also the symbolic-numeric two-point qd-algorithm to compute the poles of multivariate meromorphic functions in a given domain from its series expansion coefficients. This algorithm can be regarded as computing the parametrized eigenvalues for a tridiagonal matrix. Numerical examples are furnished to illustrate our results.
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ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-020-00887-9