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.
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About the Author
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.
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Coefficient Problems Arising from Computation of Matrix pth root
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LAP LAMBERT Academic Publishing Nov 2011, 2011
ISBN 10: 3846554316
ISBN 13: 9783846554319
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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 76 pp. Englisch. Seller Inventory # 9783846554319
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Coefficient Problems Arising from Computation of Matrix pth root
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Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Autor/Autorin: Lin MinghuaThe 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.In analyzing iterative metho. Seller Inventory # 5498686
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Coefficient Problems Arising From Computation Of Matrix Pth Root: A Master Thesis
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Coefficient Problems Arising from Computation of Matrix pth root
Published by
LAP LAMBERT Academic Publishing Nov 2011, 2011
ISBN 10: 3846554316
ISBN 13: 9783846554319
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Taschenbuch
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Taschenbuch. Condition: Neu. This item is printed on demand - Print on Demand Titel. Neuware -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.VDM Verlag, Dudweiler Landstraße 99, 66123 Saarbrücken 76 pp. Englisch. Seller Inventory # 9783846554319
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Coefficient Problems Arising from Computation of Matrix pth root : A Master Thesis
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LAP LAMBERT Academic Publishing, 2011
ISBN 10: 3846554316
ISBN 13: 9783846554319
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Taschenbuch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - 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. Seller Inventory # 9783846554319
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Coefficient Problems Arising from Computation of Matrix pth root | A Master Thesis
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Taschenbuch. Condition: Neu. Coefficient Problems Arising from Computation of Matrix pth root | A Master Thesis | Minghua Lin | Taschenbuch | 76 S. | Englisch | 2011 | LAP LAMBERT Academic Publishing | EAN 9783846554319 | Verantwortliche Person für die EU: BoD - Books on Demand, In de Tarpen 42, 22848 Norderstedt, info[at]bod[dot]de | Anbieter: preigu. Seller Inventory # 106720735