A third order iterative method for estimating the Moore-Penrose generalised inverse is developed by extending the second order iterative method described in Petković and Stanimirović (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 Petković and Stanimirović (2011), it is observed that our method gives improved performance.
Dr. Shwetabh Srivastava and Gupta, D. K., “A third order iterative method for A†”, International Journal of Computing Science and Mathematics, vol. 4, pp. 140-151, 2013.