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2014•Abstract and Applied AnalysisOpen access

A Matrix Iteration for Finding Drazin Inverse with Ninth-Order Convergence

A. S. Al-Fhaid, Stanford Shateyi, Malik Zaka Ullah, Fazlollah Soleymani

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Abstract

The aim of this paper is twofold. First, a matrix iteration for finding approximate inverses of nonsingular square matrices is constructed. Second, how the new method could be applied for computing the Drazin inverse is discussed. It is theoretically proven that the contributed method possesses the convergence rate nine. Numerical studies are brought forward to support the analytical parts.

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What this paper is about

The aim of this paper is twofold. First, a matrix iteration for finding approximate inverses of nonsingular square matrices is constructed. Second, how the new method could be applied for computing the Drazin inverse is discussed. It is theoretically proven that the contributed method possesses the convergence rate nine. Numerical studies are brought forward to support the analytical parts.

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OpenAlex reports 8 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

The aim of this paper is twofold. First, a matrix iteration for finding approximate inverses of nonsingular square matrices is constructed. Second, how the new method could be applied for computing the Drazin inverse is discussed. It is theoretically proven that the contributed method possesses the convergence rate nine. Numerical studies are brought forward to support the analytical parts.

Key concepts: Drazin inverse, Mathematics, Invertible matrix, Convergence (economics), Inverse, Matrix (chemical analysis), Rate of convergence, Order (exchange)

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