Nonnegative Interpolation (Journal of Computational Mathematics, 2021)
The problem discussed in this paper is to determine a nonnegative interpolating polynomial which takes the prescribed nonegative values $y_0,y_1,…,y_n$ at given distinct points $x_0,x_1,…,x_n$: $p(x_i)=y_i),i=0,1,…,n$. 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 $≤ m$, satisfying the above equations for any choice of $y_i≥ 0$. (2) the above equations have a unique solution in $P_{2n}^{+}$ if and only if at most one of the $y_i's$ is nonzero.