Two-point Padé approximants for Stieltjes functions and their application to composite materials - Tokarzewski, Stanisław; Telega, Józef J. (Zielona Góra: Uniwersytet Zielonogórski)
By employing special continued fractions to asymptotic expansions at zero and infinity, the convergence of the balanced and unbalanced two-point Padé approximants (2PPA) to a Stieltjes function is studied in a real domain. We prove that certain balanced and unbalanced two-point Padé approximants form a monotone sequence of upper and lower bounds uniformly converging to a Stieltjes function. The observed monotone and uniform convergence of 2PPA is exemplified in the evaluation of bounds on the effective transport coefficients of periodic inhomogeneous media.
Keywords: sterowanie; sterowanie-teoria; sztuczna inteligencja; matematyka stosowana; informatyka