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A two-step iterative method and its acceleration for outer inverses

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Abstract

A two-step iterative method and its accelerated version for approximating outer inverse \(A^{(2)}_{T,S}\) of an arbitrary matrix A are proposed. A convergence theorem for its existence is established. The rigorous error bounds are derived. Numerical experiments involving singular square, rectangular, random matrices and a sparse matrix obtained by discretization of the Poisson’s equation are solved. Iterations count, computational time and the error bounds are used to measure the performance of our method. On comparing our results with those of other iterative methods, it is seen that significantly better performance is achieved. Thus, enhanced speed and accuracy from the computational points of view has resulted for our methodology.

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Acknowledgments

The authors thank the referees for their valuable comments which have improved the presentation of the paper.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, 721802, India

    Shwetabh Srivastava & Dharmendra K Gupta

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  1. Shwetabh Srivastava
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  2. Dharmendra K Gupta
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Correspondence to Shwetabh Srivastava.

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Srivastava, S., Gupta, D.K. A two-step iterative method and its acceleration for outer inverses. Sādhanā 41, 1179–1188 (2016). https://doi.org/10.1007/s12046-016-0541-4

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  • DOI: https://doi.org/10.1007/s12046-016-0541-4

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