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.
Highlights
Drazin, in the pioneering work in [1], proposed and generalized a different type of outer inverse in associative rings and semigroups that does not possess the reflexivity feature but commutes with the element
As such, motivated by extending efficient methods of higher orders for calculating generalized inverses, here we focus on a seventh-order scheme and discuss how we can reach this higher rate by employing only five matrix by matrix products
EI (9) = 4 4 ' 1.41421, EI (12) = 7 6 ' 1.38309, EI (13) = 7 5 ' 1.47577. This shows that we have achieved our motivation by improving the efficiency index for calculating the Drazin inverse via a competitive formulation
Summary
Department of Mathematics, College of Education, University of Sulaimani, Kurdistan Region, Sulaimani 46001, Iraq Department of Mathematics, College of Science, University of Sulaimani, Kurdistan Region, Department of Mathematics, University of Venda, Private Bag X5050, Thohoyandou 0950, South Africa
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