Tracking how spurious pole-zero pairs move across Padé approximation orders lets an iterative algorithm flag inconsistent data points and reconstruct the underlying function while preserving genuine analytic structures.
Noise Effects on Pade Approximants and Conformal Maps
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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
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Analytically Consistent Reconstruction of Finite Data Using Pad\'e Sequences
Tracking how spurious pole-zero pairs move across Padé approximation orders lets an iterative algorithm flag inconsistent data points and reconstruct the underlying function while preserving genuine analytic structures.