Drazin inverse: representation, approximation, continuity and illustrations

Authors

  • S. Bendjedid University Tahar Moulay of Saida, Algeria
  • B. Messirdi High School of Electrical and Energetic Engineering-Oran, Algeria
  • S. Messirdi University of Oran1, Ahmed Ben Bella, Algeria

DOI:

https://doi.org/10.31926/but.mif.2020.13.62.2.8

Keywords:

Moore-Penrose, Drazin inverse, Generalized Drazin inverse, Representation, Approximation, Continuity

Abstract

In this paper, we present some characteristics and expressions of the Drazin inverse for matrices and bounded linear operators in Banach spaces. We give a survey of some of the results on the continuity of the Moore-Penrose and Drazin inverse, direct technics for computing the Drazin inverse are discussed, they are based on Euler-Knopp Method and characterized in terms of a limiting process. The examples presented are for illustrative purposes, some of which are provided for testing the considered iterative processes.

Author Biographies

S. Bendjedid, University Tahar Moulay of Saida, Algeria

Department of Mathematics, B.P. 128 cité ANNASR 20000

B. Messirdi, High School of Electrical and Energetic Engineering-Oran, Algeria

Laboratory of Fundamental and Applicable Mathematics of Oran (LMFAO)

S. Messirdi, University of Oran1, Ahmed Ben Bella, Algeria

Department of Mathematics, Laboratory of Fundamental and Applicable Mathematics of Oran (LMFAO)

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Published

2021-01-22

Issue

Vol. 13(62) No. 2 (2020)

Section

MATHEMATICS