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

Lin, Minghua

Brossura

ISBN 10: 3846554316 ISBN 13: 9783846554319

Casa editrice: LAP LAMBERT Academic Publishing, 2011

Riassunto

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.

Su questo libro

L'autore

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.

Dettagli dell'edizione

• Editore: LAP LAMBERT Academic Publishing
• Data di pubblicazione: 2011
• Lingua: Inglese
• ISBN 10: 3846554316
• ISBN 13: 9783846554319
• Rilegatura: Copertina flessibile
• Numero di pagine: 76
• Contatto del produttore: non disponibile
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