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An extension to rational functions of a theorem of J. L. Walsh on differences of interpolating polynomials. (English) Zbl 0485.41003

MSC:
41A05 Interpolation in approximation theory
41A10 Approximation by polynomials
41A20 Approximation by rational functions
41A21 Padé approximation
Citations:
Zbl 0447.30020
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References:
[1] G. A. BAKER Jr., Essentials of Padé Approximants, Academic Press, Inc., NewYork, 1974. Zbl0315.41014 · Zbl 0315.41014
[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 · Zbl 0447.30020
[3] [3] R. DE MONTESSUS DE BALLORE, > Sur les fractions continues algébriques, Bull. Soc. Math. France, 30 (1902), 28-36. MR1504403 JFM33.0227.01 · JFM 33.0227.01
[4] O. PERRON, Die Lehre von den Kettenbrüchen, 3rd ed., B. G. Teubner, Stuttgart, 1957. Zbl0077.06602 MR85349 · Zbl 0077.06602
[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. Zbl0241.30013 MR352475 · Zbl 0241.30013
[6] V. I. SMIRNOV and N. A. LEBEDEV, Functions of a Complex Variable, Constructive Theory, Iliffe Books Ltd., London, 1968. Zbl0164.37503 MR229803 · Zbl 0164.37503
[7] J. L. WALSH, The divergence of sequences of polynomials interpolating in roots of unity, Bull. Amer. Math. Soc, 42 (1936), 715-719. Zbl0015.34602 MR1563411 JFM62.0332.01 · Zbl 0015.34602
[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. Zbl0106.28104 MR218588 · Zbl 0106.28104
[9] D. D. WARNER, An extension of Saffs Theorem on the convergence of interpolating rational functions, J. Approximation Theory, 18 (1976), 108-418. Zbl0359.65006 MR432883 · Zbl 0359.65006
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