A Seventh-Order Scheme for Computing the Generalized Drazin Inverse

A Seventh-Order Scheme for Computing the Generalized Drazin Inverse

One of the most important generalized inverses is the Drazin inverse, which is defined for square matrices having an index. The objective of this work is to investigate and present a computational tool in the form of an iterative method for computing this task. This scheme reaches the seventh rate o...

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Main Authors: Dilan Ahmed, Mudhafar Hama, Karwan Hama Faraj Jwamer, Stanford Shateyi
Format: Article
Language:English
Published: MDPI AG 2019-07-01
Series:Mathematics
Subjects:
drazin inverse
generalized inverse
iterative methods
higher order
efficiency index
Online Access:https://www.mdpi.com/2227-7390/7/7/622
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spelling doaj-2ef3a7881c7d4d7d8e2ef81d50612acc2020-11-25T01:17:04ZengMDPI AGMathematics2227-73902019-07-017762210.3390/math7070622math7070622A Seventh-Order Scheme for Computing the Generalized Drazin InverseDilan Ahmed0Mudhafar Hama1Karwan Hama Faraj Jwamer2Stanford Shateyi3Department of Mathematics, College of Education, University of Sulaimani, Kurdistan Region, Sulaimani 46001, IraqDepartment of Mathematics, College of Science, University of Sulaimani, Kurdistan Region, Sulaimani 46001, IraqDepartment of Mathematics, College of Science, University of Sulaimani, Kurdistan Region, Sulaimani 46001, IraqDepartment of Mathematics, University of Venda, Private Bag X5050, Thohoyandou 0950, South AfricaOne of the most important generalized inverses is the Drazin inverse, which is defined for square matrices having an index. The objective of this work is to investigate and present a computational tool in the form of an iterative method for computing this task. This scheme reaches the seventh rate of convergence as long as a suitable initial matrix is chosen and by employing only five matrix products per cycle. After some analytical discussions, several tests are provided to show the efficiency of the presented formulation.https://www.mdpi.com/2227-7390/7/7/622drazin inversegeneralized inverseiterative methodshigher orderefficiency index
collection DOAJ
language English
format Article
sources DOAJ
author Dilan Ahmed
Mudhafar Hama
Karwan Hama Faraj Jwamer
Stanford Shateyi
spellingShingle Dilan Ahmed
Mudhafar Hama
Karwan Hama Faraj Jwamer
Stanford Shateyi
A Seventh-Order Scheme for Computing the Generalized Drazin Inverse
Mathematics
drazin inverse
generalized inverse
iterative methods
higher order
efficiency index
author_facet Dilan Ahmed
Mudhafar Hama
Karwan Hama Faraj Jwamer
Stanford Shateyi
author_sort Dilan Ahmed
title A Seventh-Order Scheme for Computing the Generalized Drazin Inverse
title_short A Seventh-Order Scheme for Computing the Generalized Drazin Inverse
title_full A Seventh-Order Scheme for Computing the Generalized Drazin Inverse
title_fullStr A Seventh-Order Scheme for Computing the Generalized Drazin Inverse
title_full_unstemmed A Seventh-Order Scheme for Computing the Generalized Drazin Inverse
title_sort seventh-order scheme for computing the generalized drazin inverse
publisher MDPI AG
series Mathematics
issn 2227-7390
publishDate 2019-07-01
description One of the most important generalized inverses is the Drazin inverse, which is defined for square matrices having an index. The objective of this work is to investigate and present a computational tool in the form of an iterative method for computing this task. This scheme reaches the seventh rate of convergence as long as a suitable initial matrix is chosen and by employing only five matrix products per cycle. After some analytical discussions, several tests are provided to show the efficiency of the presented formulation.
topic drazin inverse
generalized inverse
iterative methods
higher order
efficiency index
url https://www.mdpi.com/2227-7390/7/7/622
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