newton

Matrix of values of polinomials in columns

point in which the values of polynomials were got

points

Build matrix of polynimal decomposition using Newton interpolation in Newton bais:
(x-x_0), (x - x_0) * (x x_1)

Implementation of class "polyMatrix" for storing a matrix of polynomials and implements
basic matrix operations; including a determinant and characteristic polynomial.
It is based on the package 'polynom' and uses a lot of its methods to implement matrix operations.
This package includes 3 methods of triangularization of polynomial matrices:
Extended Euclidean algorithm which is most classical but numerically unstable;
Sylvester algorithm based on LQ decomposition;
Interpolation algorithm is based on LQ decomposition and Newton interpolation.
Both methods are described in
D. Henrion & M. Sebek, Reliable numerical methods for polynomial matrix triangularization,
IEEE Transactions on Automatic Control (Volume 44, Issue 3, Mar 1999, Pages 497-508) <doi:10.1109/9.751344>
and in
Salah Labhalla, Henri Lombardi & Roger Marlin,
Algorithmes de calcule de la reduction de Hermite d'une matrice a coefficients polynomeaux,
Theoretical Computer Science (Volume 161, Issue 1-2, July 1996, Pages 69-92) <doi:10.1016/0304-3975(95)00090-9>.

Nikolai Ryzhkov

polyMatrix

newton: Build matrix of polynimal decomposition using Newton interpolation in Newton bais: (x-x_0), (x - x_0) * (x x_1)

Description

Usage

Arguments

Value