(untitled) (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 pP_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.