| Titre : |
Algorithms for the factorization of matrix polynomials |
| Type de document : |
texte imprimé |
| Auteurs : |
Abdelhakim Dahimene, Auteur ; K. Hariche, Directeur de thèse |
| Editeur : |
Institut National d'Electricité et d'Electronique INELEC |
| Année de publication : |
1992 |
| Importance : |
137 f. |
| Format : |
30 cm. |
| Note générale : |
Mémoire de Magister : Electronique : Boumerdès, Institut National d'Electricité et d'Electronique INELEC : 1992
Bibliogr. f. 138 - 142 |
| Langues : |
Anglais (eng) |
| Mots-clés : |
Scalar -- polynomials Broyden's method Linear systems Quotient-difference algorithm |
| Index. décimale : |
M004292 |
| Résumé : |
The factorization (root finding) of scalar polynomials is an important tool of analysis and design for linear systems.
This thesis is a part of an ongoing effort to generalize these tools to multivariable systems via the factorization of matrix polynomials.
The main contributions of this thesis can be summarized as follows:
1/ The development of the Q.D. algorithm, which is a global method capable of producing a complete factorization of a matrix polynomial;
2/ Establishment of an existence theorem for the Q.D. algorithm;
3/ Production of convergence theorems for the Q.D. algorithm;
4/ Study of the initialization of the algorithm;
5/ Applicability of Broyden's method to matrix polynomial problems.
As a by-product, some important results have been produced:
6/ Location of the latent roots of a matrix polynomial in the complex plane;
7/ Investigation of the existence of the solvents of a monic matrix polynomial;
8/ Derivation of an incomplite partial fraction expansion of a matrix rational fraction. |
Algorithms for the factorization of matrix polynomials [texte imprimé] / Abdelhakim Dahimene, Auteur ; K. Hariche, Directeur de thèse . - Institut National d'Electricité et d'Electronique INELEC, 1992 . - 137 f. ; 30 cm. Mémoire de Magister : Electronique : Boumerdès, Institut National d'Electricité et d'Electronique INELEC : 1992
Bibliogr. f. 138 - 142 Langues : Anglais ( eng)
| Mots-clés : |
Scalar -- polynomials Broyden's method Linear systems Quotient-difference algorithm |
| Index. décimale : |
M004292 |
| Résumé : |
The factorization (root finding) of scalar polynomials is an important tool of analysis and design for linear systems.
This thesis is a part of an ongoing effort to generalize these tools to multivariable systems via the factorization of matrix polynomials.
The main contributions of this thesis can be summarized as follows:
1/ The development of the Q.D. algorithm, which is a global method capable of producing a complete factorization of a matrix polynomial;
2/ Establishment of an existence theorem for the Q.D. algorithm;
3/ Production of convergence theorems for the Q.D. algorithm;
4/ Study of the initialization of the algorithm;
5/ Applicability of Broyden's method to matrix polynomial problems.
As a by-product, some important results have been produced:
6/ Location of the latent roots of a matrix polynomial in the complex plane;
7/ Investigation of the existence of the solvents of a monic matrix polynomial;
8/ Derivation of an incomplite partial fraction expansion of a matrix rational fraction. |
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