Geodesic
From Taylor to quadratic Hermite-Padé polynomials
Electronic transactions on numerical analysis, Tome 25 (2006), pp. 480-510.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Taylor polynomials, Pad$\acute e$ approximants, and algebraic Hermite-Pad$\acute e$ approximants form a hierarchy of approximation concepts of growing complexity. In the present contribution we climb this ladder of concepts by reviewing results about the asymptotic behaviour of polynomials that are connected with the three concepts. In each case the concepts are used for the approximation of the exponential function. The review starts with a classical result by G. Szeg$\ddot o$ about the asymptotic behaviour of zeros of the Taylor polynomials, it is then continued with asymptotic results by E.B. Saff and R.S. Varga about the asymptotic behaviour of zeros and poles of Pad$\acute e$ approximants, and in the last part, analogous results are considered with respect to quadatic Hermite-Pad$\acute e$ polynomials. Here, known results are reviewed and some new ones are added. The new results are concerned with the non-diagonal case of quadatic Hermite-Pad$\acute e$ polynomials.
Classification : 41A21, 41A58, 41A63, 30B10
Keywords: Taylor series, pad$\acute e$ approximants, Hermite-pad$\acute e$ polynomials 
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     author = {Stahl, Herbert},
     title = {From {Taylor} to quadratic {Hermite-Pad\'e} polynomials},
     journal = {Electronic transactions on numerical analysis},
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     publisher = {mathdoc},
     volume = {25},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2006__25__a1/}
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Stahl, Herbert. From Taylor to quadratic Hermite-Padé polynomials. Electronic transactions on numerical analysis, Tome 25 (2006), pp. 480-510. http://geodesic.mathdoc.fr/item/ETNA_2006__25__a1/