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A new Newton’s method with diagonal Jacobian approximation for solving systems of nonlinear equations

1st Regional Conference on Applied and Engineering Mathematics (RCAEM-I) 2010 organized by Universiti Malaysia Perlis (UniMAP) and co-organized by Universiti Sains Malaysia (USM) & Universiti Kebangsaan Malaysia (UKM), 2nd - 3rd June 2010 at Eastern & Oriental Hotel, Penang.

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Bibliographic Details
Main Authors: Mohammed Waziri, Yusuf, Leong, Wah June, Malik, Abu Hassan, Mansor, Monsi
Other Authors: waziri@math.upm.edu.my,
Format: Working Paper
Language:English
Published: Universiti Malaysia Perlis (UniMAP) 2010
Subjects:
Nonlinear equations
Large scale systems
Newton’s method
Diagonal updating
Jacobian approximation
Regional Conference on Applied and Engineering Mathematics (RCAEM)
Online Access:http://dspace.unimap.edu.my/xmlui/handle/123456789/10339
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spelling my.unimap-103392010-11-28T04:24:21Z A new Newton’s method with diagonal Jacobian approximation for solving systems of nonlinear equations Mohammed Waziri, Yusuf Leong, Wah June Malik, Abu Hassan Mansor, Monsi waziri@math.upm.edu.my, leong@math.upm.edu.my Nonlinear equations Large scale systems Newton’s method Diagonal updating Jacobian approximation Regional Conference on Applied and Engineering Mathematics (RCAEM) 1st Regional Conference on Applied and Engineering Mathematics (RCAEM-I) 2010 organized by Universiti Malaysia Perlis (UniMAP) and co-organized by Universiti Sains Malaysia (USM) & Universiti Kebangsaan Malaysia (UKM), 2nd - 3rd June 2010 at Eastern & Oriental Hotel, Penang. The most prominent method for solving systems of nonlinear equations is the Newton’s method, which required computation of Jacobian matrix and solving system of n -linear equations in each of the iterations. Jacobian mostly is computationally expensive and requires evaluation (storage) of fully populated matrix of dimensionnn×. This storage qualification becomes impractical when n becomes large. The method proposed in this paper aims at reducing the storage requirement and computational cost of the Jacobian as well as CPU time. This is made possible by approximating the Jacobian into a diagonal matrix. The method is suitable for solving small, medium and large scale nonlinear systems with dense or sparse Jacobian. The convergence of the method has been proved. Numerical experiments are carried out which shows that, the proposed method is very encouraging. 2010-11-28T04:24:21Z 2010-11-28T04:24:21Z 2010-06-02 Working Paper Vol.1(15), p.104 http://hdl.handle.net/123456789/10339 en Proceedings of the 1st Regional Conference on Applied and Engineering Mathematics (RCAEM-I) 2010 Universiti Malaysia Perlis (UniMAP) Institut Matematik Kejuruteraan
institution Universiti Malaysia Perlis
building UniMAP Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Malaysia Perlis
content_source UniMAP Library Digital Repository
url_provider http://dspace.unimap.edu.my/
language English
topic Nonlinear equations
Large scale systems
Newton’s method
Diagonal updating
Jacobian approximation
Regional Conference on Applied and Engineering Mathematics (RCAEM)
spellingShingle Nonlinear equations
Large scale systems
Newton’s method
Diagonal updating
Jacobian approximation
Regional Conference on Applied and Engineering Mathematics (RCAEM)
Mohammed Waziri, Yusuf
Leong, Wah June
Malik, Abu Hassan
Mansor, Monsi
A new Newton’s method with diagonal Jacobian approximation for solving systems of nonlinear equations
description 1st Regional Conference on Applied and Engineering Mathematics (RCAEM-I) 2010 organized by Universiti Malaysia Perlis (UniMAP) and co-organized by Universiti Sains Malaysia (USM) & Universiti Kebangsaan Malaysia (UKM), 2nd - 3rd June 2010 at Eastern & Oriental Hotel, Penang.
author2 waziri@math.upm.edu.my,
author_facet waziri@math.upm.edu.my,
Mohammed Waziri, Yusuf
Leong, Wah June
Malik, Abu Hassan
Mansor, Monsi
format Working Paper
author Mohammed Waziri, Yusuf
Leong, Wah June
Malik, Abu Hassan
Mansor, Monsi
author_sort Mohammed Waziri, Yusuf
title A new Newton’s method with diagonal Jacobian approximation for solving systems of nonlinear equations
title_short A new Newton’s method with diagonal Jacobian approximation for solving systems of nonlinear equations
title_full A new Newton’s method with diagonal Jacobian approximation for solving systems of nonlinear equations
title_fullStr A new Newton’s method with diagonal Jacobian approximation for solving systems of nonlinear equations
title_full_unstemmed A new Newton’s method with diagonal Jacobian approximation for solving systems of nonlinear equations
title_sort new newton’s method with diagonal jacobian approximation for solving systems of nonlinear equations
publisher Universiti Malaysia Perlis (UniMAP)
publishDate 2010
url http://dspace.unimap.edu.my/xmlui/handle/123456789/10339
_version_ 1643789787619917824
score 13.222552

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