#### 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