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Article
On principal minors of Bezout matrix
arXiv
Document Type
Article
Publication Date
7-6-2012
Abstract
Let $x_1,...,x_{n}$ be real numbers, $P(x)=p_n(x-x_1)...(x-x_n)$, and $Q(x)$ be a polynomial of degree less than or equal to $n$. Denote by $\Delta(Q)$ the matrix of generalized divided differences of $Q(x)$ with nodes $x_1,...,x_n$ and by $B(P,Q)$ the Bezout matrix (Bezoutiant) of $P$ and $Q$. A relationship between the corresponding principal minors, counted from the right-hand lower corner, of the matrices $B(P,Q)$ and $\Delta(Q)$ is established. It implies that if the principal minors of the matrix of divided differences of a function $g(x)$ are positive or have alternating signs then the roots of the Newton's interpolation polynomial of $g$ are real and separated by the nodes of interpolation.
Disciplines
Rights
Cornell University
Citation Information
Ruben G. Hayrapetyan. "On principal minors of Bezout matrix" arXiv (2012) ISSN: 2331-8422 Available at: http://works.bepress.com/ruben-hayrapetyan/4/
https://arxiv.org/abs/1207.2434