Iterative methods for the inclusion of the inverse matrix

2014/06/20 by Petkovic, Marko D., Petkovic, Miodrag S.
#03D15 #15A09 #47J25 #65G30 #65H05 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1406.5343

Abstract

In this paper we present an efficient iterative method of order six for the inclusion of the inverse of a given regular matrix. To provide the upper error bound of the outer matrix for the inverse matrix, we combine point and interval iterations. The new method is relied on a suitable matrix identity and a modification of a hyper-power method. This method is also feasible in the case of a full-rank m× n matrix, producing the interval sequence which converges to the Moore-Penrose inverse. It is shown that computational efficiency of the proposed method is equal or higher than the methods of hyper-power's type.

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