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General order Newton-Padé approximants for multivariate functions. (English) Zbl 0513.41008

MSC:
41A21Padé approximation
41A63Multidimensional approximation problems
41A05Interpolation (approximations and expansions)
41A20Approximation by rational functions
References:
[1]Berezin, J., Zhidkov, N.: Computing methods I. New York: Addison Wesley 1965
[2]Claessens, G.: On the Newton-Padé approximation problem. J. Approximation Theory22(2), 150-160 (1978) · Zbl 0386.41002 · doi:10.1016/0021-9045(78)90062-X
[3]Claessens, G.: On the structure of the Newton-Padé table. J. Approximation Theory22(4), 304-319 (1978) · Zbl 0383.41012 · doi:10.1016/0021-9045(78)90041-2
[4]Claessens, G.: Some aspects of the rational Hermite interpolation table and its applications. Ph. D. University of Antwerp, Belgium, 1976
[5]Gasca, M., Maeztu, J.: On Lagrange and Hermite interpolation in ? k . Numer. Math.39, 1-14 (1982) · Zbl 0457.65004 · doi:10.1007/BF01399308
[6]Levin, D.: General order Padé-type rational approximants defined from double power series. J. Inst. Math. Appl.18, 1-8 (1976) · Zbl 0352.41015 · doi:10.1093/imamat/18.1.1
[7]Maeztu, J.: Interpolation de Lagrange y Hermite en ? k . Ph. D. University of Granada, Spain, 1979
[8]Salzer, H.E.: Note on osculatory rational interpolation. Math. Comput.16, 486-491 (1962) · doi:10.1090/S0025-5718-1962-0149648-7
[9]Warner, D.: Hermite interpolation with rational functions. Ph. D. University of California, San Diego, 1974
[10]Werner, H.: Remarks on Newton type multivariate Interpolation for subsets of grids. Computing25, 181-191 (1980) · Zbl 0419.65005 · doi:10.1007/BF02259644
[11]Wuytack, L.: On the osculatory rational interpolation problem. Math. Comput.29(131), 837-843 (1975) · doi:10.1090/S0025-5718-1975-0371008-3