polyMatrix-Arith

+,polyMatrix,missing-method

+,polyMatrix,polyMatrix-method

+,polyMatrix,polynomial-method

+,polyMatrix,numeric-method

+,polyMatrix,matrix-method

+,ANY,polyMatrix-method

*,polyMatrix,numeric-method

*,polyMatrix,polynomial-method

*,polyMatrix,polyMatrix-method

*,ANY,polyMatrix-method

-,polyMatrix,polyMatrix-method

-,polyMatrix,ANY-method

-,ANY,polyMatrix-method

e1, e2

These unary and binary operators perform arithmetical operations on polynomial or numerical marices.

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

Infrastructure for Manipulation Polynomial Matrices

Tamas Prohle

Peter Prohle

Ildiko Laszlo

Ulas Onat Alakent

polyMatrix-Arith function

<ul>
<li><code>+,polyMatrix,missing-method</code>: unary <code>+</code></li>
<li><code>-,polyMatrix,polyMatrix-method</code>: unary <code>-</code></li>
</ul>

Functions

Arithmetic Operators — polyMatrix-Arith

Arithmetic Operators

polyMatrix-Arith: Arithmetic Operators

Description

Usage

Arguments

Value

Functions

Details