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http://dx.doi.org/10.14317/jami.2014.171

HIGHER ORDER ITERATIONS FOR MOORE-PENROSE INVERSES  

Srivastava, Shwetabh (Department of Mathematics, IIT Kharagpur)
Gupta, D.K. (Department of Mathematics, IIT Kharagpur)
Publication Information
Journal of applied mathematics & informatics / v.32, no.1_2, 2014 , pp. 171-184 More about this Journal
Abstract
A higher order iterative method to compute the Moore-Penrose inverses of arbitrary matrices using only the Penrose equation (ii) is developed by extending the iterative method described in [1]. Convergence properties as well as the error estimates of the method are studied. The efficacy of the method is demonstrated by working out four numerical examples, two involving a full rank matrix and an ill-conditioned Hilbert matrix, whereas, the other two involving randomly generated full rank and rank deficient matrices. The performance measures are the number of iterations and CPU time in seconds used by the method. It is observed that the number of iterations always decreases as expected and the CPU time first decreases gradually and then increases with the increase of the order of the method for all examples considered.
Keywords
Moore-Penrose inverse; Random matrices; Convergence analysis; Residual; Null space; Matrix rank;
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