An Improved Diagonal Jacobian Approximation via a New Quasi-Cauchy Condition for Solving Large-Scale Systems of Nonlinear Equations

An Improved Diagonal Jacobian Approximation via a New Quasi-Cauchy Condition for Solving Large-Scale Systems of Nonlinear Equations

We present a new diagonal quasi-Newton update with an improved diagonal Jacobian approximation for solving large-scale systems of nonlinear equations. In this approach, the Jacobian approximation is derived based on the quasi-Cauchy condition. The anticipation has been to further improve the perform...

Full description

Bibliographic Details
Main Authors: Mohammed Yusuf Waziri, Zanariah Abdul Majid
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2013/875935
id doaj-2835af37de944c888f1ea502112a1365
record_format Article
spelling doaj-2835af37de944c888f1ea502112a13652020-11-25T00:53:05ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/875935875935An Improved Diagonal Jacobian Approximation via a New Quasi-Cauchy Condition for Solving Large-Scale Systems of Nonlinear EquationsMohammed Yusuf Waziri0Zanariah Abdul Majid1Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, 43400 Serdang, Selangor, MalaysiaDepartment of Mathematics, Faculty of Science, Universiti Putra Malaysia, 43400 Serdang, Selangor, MalaysiaWe present a new diagonal quasi-Newton update with an improved diagonal Jacobian approximation for solving large-scale systems of nonlinear equations. In this approach, the Jacobian approximation is derived based on the quasi-Cauchy condition. The anticipation has been to further improve the performance of diagonal updating, by modifying the quasi-Cauchy relation so as to carry some additional information from the functions. The effectiveness of our proposed scheme is appraised through numerical comparison with some well-known Newton-like methods.http://dx.doi.org/10.1155/2013/875935
collection DOAJ
language English
format Article
sources DOAJ
author Mohammed Yusuf Waziri
Zanariah Abdul Majid
spellingShingle Mohammed Yusuf Waziri
Zanariah Abdul Majid
An Improved Diagonal Jacobian Approximation via a New Quasi-Cauchy Condition for Solving Large-Scale Systems of Nonlinear Equations
Journal of Applied Mathematics
author_facet Mohammed Yusuf Waziri
Zanariah Abdul Majid
author_sort Mohammed Yusuf Waziri
title An Improved Diagonal Jacobian Approximation via a New Quasi-Cauchy Condition for Solving Large-Scale Systems of Nonlinear Equations
title_short An Improved Diagonal Jacobian Approximation via a New Quasi-Cauchy Condition for Solving Large-Scale Systems of Nonlinear Equations
title_full An Improved Diagonal Jacobian Approximation via a New Quasi-Cauchy Condition for Solving Large-Scale Systems of Nonlinear Equations
title_fullStr An Improved Diagonal Jacobian Approximation via a New Quasi-Cauchy Condition for Solving Large-Scale Systems of Nonlinear Equations
title_full_unstemmed An Improved Diagonal Jacobian Approximation via a New Quasi-Cauchy Condition for Solving Large-Scale Systems of Nonlinear Equations
title_sort improved diagonal jacobian approximation via a new quasi-cauchy condition for solving large-scale systems of nonlinear equations
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2013-01-01
description We present a new diagonal quasi-Newton update with an improved diagonal Jacobian approximation for solving large-scale systems of nonlinear equations. In this approach, the Jacobian approximation is derived based on the quasi-Cauchy condition. The anticipation has been to further improve the performance of diagonal updating, by modifying the quasi-Cauchy relation so as to carry some additional information from the functions. The effectiveness of our proposed scheme is appraised through numerical comparison with some well-known Newton-like methods.
url http://dx.doi.org/10.1155/2013/875935
work_keys_str_mv AT mohammedyusufwaziri animproveddiagonaljacobianapproximationviaanewquasicauchyconditionforsolvinglargescalesystemsofnonlinearequations
AT zanariahabdulmajid animproveddiagonaljacobianapproximationviaanewquasicauchyconditionforsolvinglargescalesystemsofnonlinearequations
AT mohammedyusufwaziri improveddiagonaljacobianapproximationviaanewquasicauchyconditionforsolvinglargescalesystemsofnonlinearequations
AT zanariahabdulmajid improveddiagonaljacobianapproximationviaanewquasicauchyconditionforsolvinglargescalesystemsofnonlinearequations
_version_ 1725239401142812672

Similar Items