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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

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
MathSciNet review: 814918
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Abstract: We estimate the error in approximating a function $ f$ by rational functions of degree $ n$ in the norm of $ {L_q}(\Omega ),\,\Omega : = {[0,\,1]^d}$. Among other things, we prove that if $ f$ is in the Sobolev space $ W_p^k(\Omega )$ and if $ k/d - 1/p + 1/q > 0$, then $ f$ can be approximated by rational functions of degree $ n$ to an order $ O({n^{ - k/d}})$.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1986-0814918-6
PII: S 0002-9947(1986)0814918-6
Keywords: Multivariate rational approximation, error estimates in $ {L_q}$, Sobolev spaces
Article copyright: © Copyright 1986 American Mathematical Society