On Local Convergence Analysis of Inexact Newton Method for Singular Systems of Equations under Majorant Condition
We present a local convergence analysis of inexact Newton method for solving singular systems of equations. Under the hypothesis that the derivative of the function associated with the singular systems satisfies a majorant condition, we obtain that the method is well defined and converges. Our analy...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
|
| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/498016 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832551897648594944 |
|---|---|
| author | Fangqin Zhou |
| author_facet | Fangqin Zhou |
| author_sort | Fangqin Zhou |
| collection | DOAJ |
| description | We present a local convergence analysis of inexact Newton method for solving singular systems of equations. Under the hypothesis that the derivative of the function associated with the singular systems satisfies a majorant condition, we obtain that the method is well defined and converges. Our analysis provides a clear relationship between the majorant function and the function associated with the singular systems. It also allows us to obtain an estimate of convergence ball for inexact Newton method and some important special cases. |
| format | Article |
| id | doaj-art-adb29335fcd1487289f7d7ea60d8e6e7 |
| institution | Kabale University |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-adb29335fcd1487289f7d7ea60d8e6e72025-02-03T06:00:08ZengWileyThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/498016498016On Local Convergence Analysis of Inexact Newton Method for Singular Systems of Equations under Majorant ConditionFangqin Zhou0Department of Mathematics and Physics, Quzhou University, Quzhou 324000, ChinaWe present a local convergence analysis of inexact Newton method for solving singular systems of equations. Under the hypothesis that the derivative of the function associated with the singular systems satisfies a majorant condition, we obtain that the method is well defined and converges. Our analysis provides a clear relationship between the majorant function and the function associated with the singular systems. It also allows us to obtain an estimate of convergence ball for inexact Newton method and some important special cases.http://dx.doi.org/10.1155/2014/498016 |
| spellingShingle | Fangqin Zhou On Local Convergence Analysis of Inexact Newton Method for Singular Systems of Equations under Majorant Condition The Scientific World Journal |
| title | On Local Convergence Analysis of Inexact Newton Method for Singular Systems of Equations under Majorant Condition |
| title_full | On Local Convergence Analysis of Inexact Newton Method for Singular Systems of Equations under Majorant Condition |
| title_fullStr | On Local Convergence Analysis of Inexact Newton Method for Singular Systems of Equations under Majorant Condition |
| title_full_unstemmed | On Local Convergence Analysis of Inexact Newton Method for Singular Systems of Equations under Majorant Condition |
| title_short | On Local Convergence Analysis of Inexact Newton Method for Singular Systems of Equations under Majorant Condition |
| title_sort | on local convergence analysis of inexact newton method for singular systems of equations under majorant condition |
| url | http://dx.doi.org/10.1155/2014/498016 |
| work_keys_str_mv | AT fangqinzhou onlocalconvergenceanalysisofinexactnewtonmethodforsingularsystemsofequationsundermajorantcondition |