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Více informací o knize Coefficient Problems Arising from Computation of Matrix pth root

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• Anotace
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Anotace knihy

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.

Parametry knihy

• Plný název: Coefficient Problems Arising from Computation of Matrix pth root
• Podnázev: A Master Thesis
• Autor: Minghua Lin
• Jazyk: Angličtina
• Vazba: Brožovaná
• Počet stran: 76
• EAN: 9783846554319
• ID: 06995938
• Nakladatelství: LAP Lambert Academic Publishing
• Hmotnost: 130 g
• Rozměry: 220 × 150 × 5 mm
• Rok vydání: 2011

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