Title: A third order iterative method for A^†

Authors: Shwetabh Srivastava; D.K. Gupta

Addresses: Department of Mathematics, Indian Institute of Technology, Kharagpur 721 302, West Bengal, India ' Department of Mathematics, Indian Institute of Technology, Kharagpur 721 302, West Bengal, India

Abstract: A third order iterative method for estimating the Moore-Penrose generalised inverse is developed by extending the second order iterative method described in Petkovi and Stanimirovi (2011). Convergence analysis along with the error estimates of the method are investigated. Three numerical examples, two for full rank simple and randomly generated singular rectangular matrices and third for rank deficient singular square matrices with large condition numbers from the matrix computation toolbox are worked out to demonstrate the efficacy of the method. The performance measures used are the number of iterations and CPU time used by the method. On comparing the results obtained by our method with those obtained with the method given in Petkovi and Stanimirovi (2011), it is observed that our method gives improved performance.

Keywords: Moore-Penrose generalised inverse; CPU time; convergence analysis; residual; singular matrices; condition numbers; third order iterative method.

DOI: 10.1504/IJCSM.2013.055209

International Journal of Computing Science and Mathematics, 2013 Vol.4 No.2, pp.140 - 151

Received: 27 Nov 2012
Accepted: 28 Mar 2013
Published online: 10 May 2014 *

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