polyMatrix-package {polyMatrix} | R Documentation |
Implementation of matrices of polynomials
Description
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>.
Details
This package add transperent support of matrices of polynomials to R language.
Input
low level input of matrix:
polyMatrix()
string ibpuy of polynomial:
parse.polynomial()
string input of matrix:
parse.polyMatrix()
Output
Matrices of polynomials uses same format as numerical matrices
Operators
Basic arithmetic operations were implemented.
Functions
The most important matrix functions are implemented:
the determinant
det()
Author(s)
Maintainer: Nikolai Ryzhkov namezys@gmail.com (ORCID)
Authors:
Tamas Prohle prohlet@ludens.elte.hu
Peter Prohle prohlep@math.elte.hu
Ildiko Laszlo (ORCID)
Other contributors:
Ulas Onat Alakent [contributor]
See Also
Useful links: