| Issue |
ITM Web Conf.
Volume 24, 2019
AMCSE 2018 - International Conference on Applied Mathematics, Computational Science and Systems Engineering
|
|
|---|---|---|
| Article Number | 01008 | |
| Number of page(s) | 5 | |
| Section | Communications-Systems-Signal Processing | |
| DOI | https://doi.org/10.1051/itmconf/20192401008 | |
| Published online | 01 February 2019 | |
A particular block Vandermonde matrix
1
Laboratoire LTII, University of Bejaia, Algeria
2
IGEE Institute, University of Boumerdes, Algeria
* Corresponding author: yaici_m@hotmail.com
The Vandermonde matrix is ubiquitous in mathematics and engineering. Both the Vandermonde matrix and its inverse are often encountered in control theory, in the derivation of numerical formulas, and in systems theory. In some cases block vandermonde matrices are used. Block Vandermonde matrices, considered in this paper, are constructed from a full set of solvents of a corresponding matrix polynomial. These solvents represent block poles and block zeros of a linear multivariable dynamical time-invariant system described in matrix fractions. Control techniques of such systems deal with the inverse or determinant of block vandermonde matrices. Methods to compute the inverse of a block vandermonde matrix have not been studied but the inversion of block matrices (or partitioned matrices) is very well studied. In this paper, properties of these matrices and iterative algorithms to compute the determinant and the inverse of a block Vandermonde matrix are given. A parallelization of these algorithms is also presented. The proposed algorithms are validated by a comparison based on algorithmic complexity.
© The Authors, published by EDP Sciences, 2019
This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0 (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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