Multivariate rational approximation
Authors:
Ronald A. DeVore and Xiang Ming Yu
Journal:
Trans. Amer. Math. Soc. 293 (1986), 161169
MSC:
Primary 41A20; Secondary 41A63
MathSciNet review:
814918
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Abstract: We estimate the error in approximating a function by rational functions of degree in the norm of . Among other things, we prove that if is in the Sobolev space and if , then can be approximated by rational functions of degree to an order .
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 Yu. Brudnyi, Rational approximation and exotic Lipschitz spaces, in [4, pp. 2530]. MR 588168 (82f:41022)
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 M. S. Birman and M. Solomjak, Piecewisepolynomial approximation of functions of the classes , Math. USSRSb. 2 (1967), 295317. MR 0217487 (36:576)
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 R. A. DeVore, Maximal functions and their application to rational approximation, CBMS Regional Conf. Ser. Math., no. 3, Amer. Math. Soc., Providence, R. I., 1983, pp. 143155. MR 729327 (85g:41022)
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 R. A. DeVore and K. Scherer (editors), Quantitative approximation, Academic Press, New York, 1980. MR 588164 (81i:41001)
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 R. A. DeVore and R. C. Sharpley, Maximal functions measuring smoothness, Mem. Amer. Math. Soc., Vol. 47, No. 293, 1984. MR 727820 (85g:46039)
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 G. G. Lorentz, Approximation of functions, Holt, New York, 1966, p. 94. MR 0213785 (35:4642)
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 D. J. Newman, Rational approximation to , Michigan Math. J. 11 (1964), 1114. MR 0171113 (30:1344)
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 V. Popov, Uniform rational approximation of the class and its applications, Acta Math. Acad. Sci. Hungar. 29 (1977), 119129. MR 0435679 (55:8637)
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 , On the connection between rational uniform approximation and polynomial approximation of functions, in [4, 267277]. MR 588187 (81j:41025)
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 S. L. Sobolev, Applications of functional analysis in mathematical physics, Transl. Math. Monos., vol. 7, Amer. Math. Soc., Providence, R. I., 1963.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947198608149186
PII:
S 00029947(1986)08149186
Keywords:
Multivariate rational approximation,
error estimates in ,
Sobolev spaces
Article copyright:
© Copyright 1986 American Mathematical Society
