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Stable polefinding and rational least-squares fitting via eigenvalues

Abstract:

A common way of finding the poles of a meromorphic function f in a domain, where an explicit expression of f is unknown but f can be evaluated at any given z, is to interpolate f by a rational function pq such that r(γi)=f(γi) at prescribed sample points {γi}Li=1 , and then find the roots of q. This is a two-step process and the type of the rational interpolant needs to be specified by the user. Many other algorithms for polefinding and rational interpolation (or least-squares fitting...

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Publication status:
Published
Peer review status:
Peer reviewed
Version:
Publisher's Version

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Publisher copy:
10.1007/s00211-018-0948-4

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Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Oxford college:
Christ Church
Publisher:
Springer Publisher's website
Journal:
Numerische Mathematik Journal website
Volume:
139
Issue:
3
Pages:
633-682
Publication date:
2018-02-21
Acceptance date:
2018-01-14
DOI:
EISSN:
0945-3245
ISSN:
0029-599X
Pubs id:
pubs:993764
URN:
uri:0508eab6-abc2-45f1-ac55-998a51da82fb
UUID:
uuid:0508eab6-abc2-45f1-ac55-998a51da82fb
Local pid:
pubs:993764
Language:
English
Keywords:

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