Titlebook: Approximation Theory. Tampa; Proceedings of a Sem Edward B. Saff Conference proceedings 1987 Springer-Verlag Berlin Heidelberg 1987 Approxi

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rods366

Zero-free disks in families of analytic functions,Newton’s method will be described. The problem arises in several fields of approximation theory, notably in connection with certain Padé approximants and with the Whittaker and the power series constants. Conjectured values of these constants will be given in extended precision.

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,Boundary collocation in Fejér points for computing eigenvalues and eigenfunctions of the Laplacian,ex regions rapid convergence generally can be achieved only if the eigenfunctions are approximated by functions with singular points in the finite plane. A boundary collocation method with such basis functions is also described.

Bernstein-test

,A fast algorithm to solve Kalman’s partial realisation problem for single input, multi-output systect analogues of Baker’s and Kronecker’s algorithms. These analogues are fast algorithms for simultaneous Padé approximation of two series, and so also for a solution of the single input, two output partial realisation problem.

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Ordnance

Ergebnisse der Chirurgie und Orthop?dien the solution of the single input, multi-output partial realisation problem is then discussed. We show how analogues of Frobenius identities are derived for simultaneous Padé approximants of two series, and we give twelve such identities. We show how some of these identities are combined to constru

Enrage

Ergebnisse der Chirurgie und Orthop?die asymptotics for the associated recurrence relation coefficients, analogous to those obtained recently for weights such as exp(?|x|.), α>0. Our results apply to weights such as W(x) ?exp(?exp(|x|.)) or W(x) ?exp(?exp(exp(|x|.))), α>0 arbitrary..As a preliminary step, we investigate the possibility o