# Best polynomial approximation on the triangle

@article{Feng2019BestPA,
title={Best polynomial approximation on the triangle},
author={Han Feng and Christian Krattenthaler and Yuan Xu},
journal={J. Approx. Theory},
year={2019},
volume={241},
pages={63-78}
}
• Published 13 November 2017
• Computer Science, Mathematics
• J. Approx. Theory
Let $E_n(f)_{\alpha,\beta,\gamma}$ denote the error of best approximation by polynomials of degree at most $n$ in the space $L^2(\varpi_{\alpha,\beta,\gamma})$ on the triangle $\{(x,y): x, y \ge 0, x+y \le 1\}$, where $\varpi_{\alpha,\beta,\gamma}(x,y) := x^\alpha y ^\beta (1-x-y)^\gamma$ for $\alpha,\beta,\gamma > -1$. Our main result gives a sharp estimate of $E_n(f)_{\alpha,\beta,\gamma}$ in terms of the error of best approximation for higher order derivatives of $f$ in appropriate Sobolev… Expand
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