Year: 1984
Journal of Computational Mathematics, Vol. 2 (1984), Iss. 4 : pp. 328–330
Abstract
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 $y_i's$ is nonzero.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/1984-JCM-9668
Journal of Computational Mathematics, Vol. 2 (1984), Iss. 4 : pp. 328–330
Published online: 1984-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 3