Multivariate rational approximation

Authors:
Ronald A. DeVore and Xiang Ming Yu

Journal:
Trans. Amer. Math. Soc. **293** (1986), 161-169

MSC:
Primary 41A20; Secondary 41A63

DOI:
https://doi.org/10.1090/S0002-9947-1986-0814918-6

MathSciNet review:
814918

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Abstract | References | Similar Articles | Additional Information

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 .

**[1]**Yu. Brudnyi,*Rational approximation and exotic Lipschitz spaces*, in [**4**, pp. 25-30]. MR**588168 (82f:41022)****[2]**M. S. Birman and M. Solomjak,*Piecewise-polynomial approximation of functions of the classes*, Math. USSR-Sb.**2**(1967), 295-317. MR**0217487 (36:576)****[3]**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. 143-155. MR**729327 (85g:41022)****[4]**R. A. DeVore and K. Scherer (editors),*Quantitative approximation*, Academic Press, New York, 1980. MR**588164 (81i:41001)****[5]**R. A. DeVore and R. C. Sharpley,*Maximal functions measuring smoothness*, Mem. Amer. Math. Soc., Vol. 47, No. 293, 1984. MR**727820 (85g:46039)****[6]**G. G. Lorentz,*Approximation of functions*, Holt, New York, 1966, p. 94. MR**0213785 (35:4642)****[7]**D. J. Newman,*Rational approximation to*, Michigan Math. J.**11**(1964), 11-14. MR**0171113 (30:1344)****[8]**V. Popov,*Uniform rational approximation of the class**and its applications*, Acta Math. Acad. Sci. Hungar.**29**(1977), 119-129. MR**0435679 (55:8637)****[9]**-,*On the connection between rational uniform approximation and polynomial**approximation of functions*, in [**4**, 267-277]. MR**588187 (81j:41025)****[10]**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:
https://doi.org/10.1090/S0002-9947-1986-0814918-6

Keywords:
Multivariate rational approximation,
error estimates in ,
Sobolev spaces

Article copyright:
© Copyright 1986
American Mathematical Society