Noise effects on Padé approximants and conformal maps

• Published in: Journal 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
• Language: English
• Published: United States IOP Publishing 18.11.2022
• Subjects: conformal maps; MATHEMATICS AND COMPUTING; noise; Pade approximants; Painleve; quantum field theory

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...