Title
The relationship between Bézoutian matrix and Newton’s matrix of divided differences
Document Type
Article
Publication Date
7-1-2010
Publication Title
Progress in Analysis and its Applications
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 order less than or equal to n. Denote by Δ(Q) the matrix of generalized divided differences of Q(x) with nodes x 1 ,...,x n and by B(P,Q) the Bézoutian matrix of P and Q. A relationship between the corresponding principal minors of the matrices B(P,Q) and Δ(Q) counted from the right lower corner 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.
First Page
584
Last Page
597
DOI
https://doi.org/10.1142/9789814313179_0075
ISSN
0218-2025
Rights
World Scientific
Recommended Citation
Hayrapetyan, Ruben G., "The relationship between Bézoutian matrix and Newton’s matrix of divided differences" (2010). Mathematics Publications. 78.
https://digitalcommons.kettering.edu/mathematics_facultypubs/78
Comments
ESSN: 1793-6314