2 research outputs found
On principal minors of Bezout matrix
Let be real numbers, , and
be a polynomial of degree less than or equal to . Denote by the
matrix of generalized divided differences of with nodes
and by the Bezout matrix (Bezoutiant) of and . A relationship
between the corresponding principal minors, counted from the right-hand lower
corner, of the matrices and is established. It implies
that if the principal minors of the matrix of divided differences of a function
are positive or have alternating signs then the roots of the Newton's
interpolation polynomial of are real and separated by the nodes of
interpolation.Comment: 15 page
Multivariate Subresultants in Roots
We give rational expressions for the subresultants of n+1 generic polynomials
f_1,..., f_{n+1} in n variables as a function of the coordinates of the common
roots of f_1,..., f_n and their evaluation in f_{n+1}. We present a simple
technique to prove our results, giving new proofs and generalizing the
classical Poisson product formula for the projective resultant, as well as the
expressions of Hong for univariate subresultants in roots.Comment: 22 pages, no figures, elsart style, revised version of the paper
presented in MEGA 2005, accepted for publication in Journal of Algebr