Noise Effects on Pade Approximants and Conformal Maps

Abstract

We analyze the properties of Pade 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 Pade 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

arXiv comment23 pages, 8 figures

References in corpus (17)

• 2D Gravity and Random Matrices
• Renormalization in quantum field theory and the Riemann-Hilbert problem I: the Hopf algebra structure of graphs and the main theorem
• Renormalization in quantum field theory and the Riemann-Hilbert problem II: the $\beta$-function, diffeomorphisms and the renormalization group
• Exact solutions of Dyson-Schwinger equations for iterated one-loop integrals and propagator-coupling duality
• Five loop renormalization of ${\varphi }^3$ theory with applications to the Lee-Yang edge singularity and percolation theory
• Physical Resurgent Extrapolation
• Combinatoric explosion of renormalization tamed by Hopf algebra: 30-loop Pade-Borel resummation
• Pade approximants for functions with branch points - strong asymptotics of Nuttall-Stahl polynomials
• Resurgent Extrapolation: Rebuilding a Function from Asymptotic Data. Painleve I
• Jost Functions and Jost Solutions for Jacobi Matrices, I. A Necessary and Sufficient Condition for Szego Asymptotics
• Proof of the Dubrovin conjecture and analysis of the tritronquée solutions of $P_I$
• Logarithmic Potential Theory with Applications to Approximation Theory
• Uniformization and Constructive Analytic Continuation of Taylor Series
• Conformal and Uniformizing Maps in Borel Analysis
• Universal analytic properties of noise. Introducing the J-Matrix formalism
• On the convergence on nonlinear Padé--Chebyshev approximations to the multivalued analytic functions, variation of equilibrium energy and $S$-property of stationary compacts
• Semiclassical Trans-Series from the Perturbative Hopf-Algebraic Dyson-Schwinger Equations: ${\varphi }^3$ QFT in 6 Dimensions

Cited by in corpus (2)

• Exploring Lee-Yang and Fisher Zeros in the 2D Ising model through multipoint Padé approximants
• Exponential Asymptotics using Numerical Rational Approximation in Linear Differential Equations