International Journal of applied mathematics and computer science

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Paper details

Number 2 - June 1998
Volume 8 - 1998

Two-point Padé approximants for Stieltjes functions and their application to composite materials

Stanisław Tokarzewski, Józef J. Telega

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.