An extension to rational functions of a theorem of J. L. Walsh on differences of interpolating polynomials

E. B. Saff; A. Sharma; R. S. Varga

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1981)

  • Volume: 15, Issue: 4, page 371-390
  • ISSN: 0764-583X

How to cite

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Saff, E. B., Sharma, A., and Varga, R. S.. "An extension to rational functions of a theorem of J. L. Walsh on differences of interpolating polynomials." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 15.4 (1981): 371-390. <http://eudml.org/doc/193387>.

@article{Saff1981,
author = {Saff, E. B., Sharma, A., Varga, R. S.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {interpolating meromorphic functions},
language = {eng},
number = {4},
pages = {371-390},
publisher = {Dunod},
title = {An extension to rational functions of a theorem of J. L. Walsh on differences of interpolating polynomials},
url = {http://eudml.org/doc/193387},
volume = {15},
year = {1981},
}

TY - JOUR
AU - Saff, E. B.
AU - Sharma, A.
AU - Varga, R. S.
TI - An extension to rational functions of a theorem of J. L. Walsh on differences of interpolating polynomials
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1981
PB - Dunod
VL - 15
IS - 4
SP - 371
EP - 390
LA - eng
KW - interpolating meromorphic functions
UR - http://eudml.org/doc/193387
ER -

References

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  1. [1] G. A. BAKER Jr., Essentials of Padé Approximants, Academic Press, Inc., NewYork, 1974. Zbl0315.41014
  2. [2] A. S. CAVARETTA Jr., A. SHARMA and R. S. VARGA, Interpolation in the roots of unity : an extension of a Theorem of I. L. Walsh, Resultate der Mathematik, 3 (1981), 155-191. Zbl0447.30020
  3. [3] R. DE MONTESSUS DE BALLORE, &gt; Sur les fractions continues algébriques, Bull. Soc. Math. France, 30 (1902), 28-36. MR1504403JFM33.0227.01
  4. [4] O. PERRON, Die Lehre von den Kettenbrüchen, 3rd ed., B. G. Teubner, Stuttgart, 1957. Zbl0077.06602MR85349
  5. [5] E. B. SAFF, An extension of Montessus de Ballore's Theorem on the convergence of interpolating rational functions, J. Approximation Theory, 6 (1972), 63-67. Zbl0241.30013MR352475
  6. [6] V. I. SMIRNOV and N. A. LEBEDEV, Functions of a Complex Variable, Constructive Theory, Iliffe Books Ltd., London, 1968. Zbl0164.37503MR229803
  7. [7] J. L. WALSH, The divergence of sequences of polynomials interpolating in roots of unity, Bull. Amer. Math. Soc, 42 (1936), 715-719. Zbl0015.34602MR1563411JFM62.0332.01
  8. [8] J. L. WALSH, Interpolation and Approximation by Rational Functions in the Comple Domain, 5th éd., Colloq. Publ. Vol. 20, American Mathematical Society, Providence, R.I., 1969. Zbl0106.28104MR218588
  9. [9] D. D. WARNER, An extension of Saffs Theorem on the convergence of interpolating rational functions, J. Approximation Theory, 18 (1976), 108-418. Zbl0359.65006MR432883

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