Coefficient Problems Arising from Computation of Matrix pth root: A Master Thesis - Couverture souple

Lin, Minghua

 
9783846554319: Coefficient Problems Arising from Computation of Matrix pth root: A Master Thesis
Couverture souple
ISBN 10 : 3846554316 ISBN 13 : 9783846554319
Editeur : LAP LAMBERT Academic Publishing, 2011

Synopsis

In analyzing iterative methods (eg. Newton’s method and Halley’s method) for the principal pth root of a matrix, we come across some coefficient problems. These problems are in the form of determining the signs of Taylor coefficients of certain functions or function sequences. The former is relatively easy, while the latter is much more difficult. This thesis mainly deals with a conjecture on this aspect raised by Dr. Chun-Hua Guo. The validity of the conjecture will give neat error estimates of the proposed algorithms. Concerning this, I obtain a simple unified proof of the conjecture for principal square root of a matrix. Other partial results are also presented.For example, using order estimate method, I am able to determine the sign of more coefficients for Newton’s method and Halley’s method, respectively. Some closely related problems are also addressed. For example, I give an affirmative answer to a conjecture on a residual relation for pth root of complex numbers using first derivative technique. The first derivative technique is also used to obtain a simple proof of residual relations for Halley’s method.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

In analyzing iterative methods (eg. Newton’s method and Halley’s method) for the principal pth root of a matrix, we come across some coefficient problems. These problems are in the form of determining the signs of Taylor coefficients of certain functions or function sequences. The former is relatively easy, while the latter is much more difficult. This thesis mainly deals with a conjecture on this aspect raised by Dr. Chun-Hua Guo. The validity of the conjecture will give neat error estimates of the proposed algorithms. Concerning this, I obtain a simple unified proof of the conjecture for principal square root of a matrix. Other partial results are also presented.For example, using order estimate method, I am able to determine the sign of more coefficients for Newton’s method and Halley’s method, respectively. Some closely related problems are also addressed. For example, I give an affirmative answer to a conjecture on a residual relation for pth root of complex numbers using first derivative technique. The first derivative technique is also used to obtain a simple proof of residual relations for Halley’s method.

Biographie de l'auteur

The author did his master's study at the Univeristy of Regina. The thesis presents his research on coefficient patterns of certain iterations arising from the computation of matrix pth root.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
LAP LAMBERT Academic Publishing
Date d'édition
2011
Langue
anglais
ISBN 10 
3846554316
ISBN 13 
9783846554319
Reliure
Broché
Nombre de pages
76
Coordonnées du fabricant
non disponible
Personne responsable
KreGa Onlinehandel GmbH
4950000000000
info@krega-onlinehandel.de

Birkenweg 31
Brakel
33034
Allemagne