A Seventh-Order Scheme for Computing the Generalized Drazin Inverse

Dilan Ahmed, Mudhafar Hama, Karwan Hama Faraj Jwamer and Stanford Shateyi
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Dilan Ahmed: Department of Mathematics, College of Education, University of Sulaimani, Kurdistan Region, Sulaimani 46001, Iraq
Mudhafar Hama: Department of Mathematics, College of Science, University of Sulaimani, Kurdistan Region, Sulaimani 46001, Iraq
Karwan Hama Faraj Jwamer: Department of Mathematics, College of Science, University of Sulaimani, Kurdistan Region, Sulaimani 46001, Iraq
Stanford Shateyi: Department of Mathematics, University of Venda, Private Bag X5050, Thohoyandou 0950, South Africa

Mathematics, 2019, vol. 7, issue 7, 1-10

Abstract: 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.

Keywords: drazin inverse; generalized inverse; iterative methods; higher order; efficiency index (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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