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Exponential node clustering at singularities for rational approximation, quadrature, and PDEs

Abstract:

Rational approximations of functions with singularities can converge at a root-exponential rate if the poles are exponentially clustered. We begin by reviewing this effect in minimax, least-squares, and AAA approximations on intervals and complex domains, conformal mapping, and the numerical solution of Laplace, Helmholtz, and biharmonic equations by the "lightning" method. Extensive and wide-ranging numerical experiments are involved. We then present further experiments showing that in all o...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1007/s00211-020-01168-2

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More by this author
Institution:
University of Oxford
Department:
MATHEMATICAL INSTITUTE
Subgroup:
Mathematical Institute
Oxford college:
Balliol College
Role:
Author
ORCID:
0000-0003-2504-1709
More by this author
Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
Christ Church
Role:
Author
ORCID:
0000-0001-7911-1501
Publisher:
Springer Publisher's website
Journal:
Numerische Mathematik Journal website
Publication date:
2021-01-02
Acceptance date:
2020-11-19
DOI:
EISSN:
0945-3245
ISSN:
0029-599X
Pubs id:
1123281
Local pid:
pubs:1123281

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