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 in | Journal of physics. A, Mathematical and theoretical Vol. 55; no. 46; pp. 464007 - 464027 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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United States
IOP Publishing
18.11.2022
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| ISSN | 1751-8113 1751-8121 |
| DOI | 10.1088/1751-8121/aca303 |
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| Abstract | 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. |
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| AbstractList | 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. Here, 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. |
| Author | Dunne, Gerald V Costin, Ovidiu Meynig, Max |
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| Cites_doi | 10.1016/j.physletb.2020.135627 10.1070/RM2011v066n06ABEH004770 10.1090/conm/578/11474 10.1016/0377-0427(95)00177-8 10.1016/S0377-0427(97)00185-4 10.1103/PhysRevD.103.116024 10.1016/j.nuclphysb.2022.115861 10.1016/0370-1573(94)00084-G 10.1016/S0370-2693(00)00051-4 10.1088/0305-4470/14/9/034 10.1016/0550-3213(79)90086-5 10.1007/s11511-016-0133-5 10.1016/S0377-0427(02)00674-X 10.1137/0506024 10.1140/epjs/s11734-021-00267-x 10.1006/jath.1997.3141 10.1016/S0377-0427(99)00041-2 10.1070/RM2011v066n06ABEH004769 10.1088/1751-8113/42/36/365202 10.1103/PhysRevLett.40.1610 10.3842/SIGMA.2021.087 10.1007/s00222-005-0485-5 10.1088/1751-8121/ab477b 10.1007/s00332-008-9025-y 10.1007/BF03321780 10.1007/PL00005547 10.1007/s00220-022-04361-6 10.1007/s002200050779 10.1016/S0550-3213(01)00071-2 10.1215/00127094-2429589 |
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| Snippet | We analyze the properties of Padé and conformal map approximants for functions with branch points, in the situation where the expansion coefficients are only... Here, we analyze the properties of Padé and conformal map approximants for functions with branch points, in the situation where the expansion coefficients are... |
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| SubjectTerms | conformal maps MATHEMATICS AND COMPUTING noise Pade approximants Painleve quantum field theory |
| Title | Noise effects on Padé approximants and conformal maps |
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