@Article{JCM-2-328,
author = {Ying-Guang Shi},
title = {Nonnegative Interpolation},
journal = {Journal of Computational Mathematics},
year = {1984},
volume = {2},
number = {4},
pages = {328--330},
abstract = {<p style="text-align: justify;">The problem discussed in this paper is to determine a nonnegative interpolating polynomial which takes the prescribed nonegative values $y_0,y_1,\cdots,y_n$ at given distinct points $x_0,x_1,\cdots,x_n$: $p(x_i)=y_i),i=0,1,\cdots,n$. This paper shows：(1) $2n$ is the least number of $m$ such that there exists a polynomial $p\in P_m^{+}$, the set of all nonnegative polynomials of degree $\leq m$, satisfying the above equations for any choice of $y_i\geq 0$. (2) the above equations have a unique solution in $P_{2n}^{+}$ if and only if at most one of the $y_i&#39;s$ is nonzero.</p>},
issn = {1991-7139},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/jcm/9668.html}
}