Noise effects on Padé approximants and conformal maps

We analyze the properties of Padé and conformal map approximants for functions with branch points, in the situation where the expansion coefficients are only known with finite precision or are subject to noise. We prove that there is a universal scaling relation between the strength of the noise and...

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Published inJournal of physics. A, Mathematical and theoretical Vol. 55; no. 46; pp. 464007 - 464027
Main Authors Costin, Ovidiu, Dunne, Gerald V, Meynig, Max
Format Journal Article
LanguageEnglish
Published United States IOP Publishing 18.11.2022
Subjects
conformal maps
MATHEMATICS AND COMPUTING
noise
Pade approximants
Painleve
quantum field theory
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Summary:We analyze the properties of Padé and conformal map approximants for functions with branch points, in the situation where the expansion coefficients are only known with finite precision or are subject to noise. We prove that there is a universal scaling relation between the strength of the noise and the expansion order at which Padé or the conformal map breaks down. We illustrate this behavior with some physically relevant model test functions and with two non-trivial physical examples where the relevant Riemann surface has complicated structure.
Bibliography:JPhysA-117919.R1
SC0010339
USDOE Office of Science (SC), High Energy Physics (HEP)
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8121/aca303