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An iterative method for solving singular linear systems with index one

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Abstract

An iterative method along with its convergence analysis is developed for solving singular linear systems with index one. Necessary and sufficient conditions along with the estimation of error bounds for the unique solution are derived. Four numerical examples including singular square M-matrix, randomly generated singular square matrices, sparse symmetric and nonsymmetric singular matrices obtained from discretization of the special partial differential equations are worked out. A comparison between proposed method and method from Chen (Appl Math Comput 86:171–184, 1997) is given in terms of number of iterations, mean CPU time and error bounds. It is observed that proposed iterative method is superior and gives improved performance when compared with the method from Chen (Appl Math Comput 86:171–184, 1997).

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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, 721302, India

    S. Srivastava & D. K. Gupta

  2. Department of Geology and Geophysics, Indian Institute of Technology, Kharagpur, 721302, India

    A. Singh

Authors
  1. S. Srivastava
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  2. D. K. Gupta
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  3. A. Singh
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Corresponding author

Correspondence to S. Srivastava.

Appendix

Appendix

In this section we state the algorithm and its matlab code implementation to compute the group inverse solution of (1).

figure a

The Matlab implementation of Algorithm 1 by matlab function gisolution is given below.

figure b

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Srivastava, S., Gupta, D.K. & Singh, A. An iterative method for solving singular linear systems with index one. Afr. Mat. 27, 815–824 (2016). https://doi.org/10.1007/s13370-015-0379-7

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