Multivariate rational approximation
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- by Ronald A. DeVore and Xiang Ming Yu PDF
- Trans. Amer. Math. Soc. 293 (1986), 161-169 Request permission
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 $O({n^{ - k/d}})$.References
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Additional Information
- © Copyright 1986 American Mathematical Society
- 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