Abstract
The existence of valleys formed by level curves of quasi-equal elements in the c-table, observed at first in [1], is proved for the non-rational Stieltjes functions and for the exponential function. The same is also proved for the table of ratios of Toeplitz determinants which characterize the behaviour at the origin of the difference between a function and its Padé approximant. The optimal method of recursive computation of the c-table with blocks is presented.
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References
GILEWICZ, J. "Approximants de Padé", Lecture Notes in Mathematics, 667, Springer-Verlag (1978).
AITKEN, A.C. "Determinants and Matrices", Oliver & Boyd, Edinburgh (1946).
BREZINSKI, C. "Accélération de la convergence en analyse numérique", Lecture Notes in Mathematics, 584, Springer-Verlag (1977).
GUZINSKI, W. "PADELIB: Library of Padé Approximation Routines", TNR 1768, Institute of Nuclear Research, Warsaw (1978).
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© 1979 Springer-Verlag
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Gilewicz, J., Magnus, A. (1979). Valleys in c-table. In: Wuytack, L. (eds) Padé Approximation and its Applications. Lecture Notes in Mathematics, vol 765. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0085578
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DOI: https://doi.org/10.1007/BFb0085578
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-09717-4
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