In this paper we use the Moore-Penrose inverse in the case of a close to singular and ill-conditioned, or singular variance-covariance matrix, in the classic Portfolio Selection Problem. In this way the possible singularity of the variance-covariance matrix is tackled in an efficient way so that the various application of the Problem to benefit from the numerical tractability of the Moore-Penro...

This paper presents a recursive procedure to compute the Moore-Penrose inverse of a matrix A. The method is based on the expression for the Moore-Penrose inverse of rank-one modified matrix. The computational complexity of the method is analyzed and a numerical example is included. A variant of the algorithm with lower computational complexity is also proposed. Both algorithms are tested on ran...

The goal of this paper is to present an accelerated iterative method for computing weighted Moore–Penrose inverse. Analysis of convergence is included to show that the proposed scheme has sixth-order convergence. Using a proper initial matrix, a sequence of iterates will be produced, which is convergent to the weighted Moore–Penrose inverse. Numerical experiments are reported to show the effici...

In this paper, a link between the Hyers–Ulam stability and the Moore–Penrose inverse is established, that is, a closed operator has the Hyers–Ulam stability if and only if it has a bounded Moore–Penrose inverse. Meanwhile, the stability constant can be determined in terms of the Moore– Penrose inverse. Based on this result, some conditions for the perturbed operators having the Hyers– Ulam stab...

We study generalized inverses on semigroups by means of Green’s relations. We first define the notion of inverse along an element and study its properties. Then we show that the classical generalized inverses (group inverse, Drazin inverse and Moore-Penrose inverse) belong to this class. There exist many specific generalized inverses in the literature, such as the group inverse, the Moore-Penro...

In this paper we construct a few iterative processes for computing {1, 2} inverses of a linear bounded operator, based on the hyper-power iterative method or the Neumann-type expansion. Under the suitable conditions these methods converge to the {1, 2, 3} or {1, 2, 4} inverses. Also, we specify conditions when the iterative processes converge to the Moore-Penrose inverse, the weighted Moore-Pen...

in this paper, we state some results on product of operators with closed rangesand we solve the operator equation txs*- sx*t*= a in the general setting of theadjointable operators between hilbert c*-modules, when ts = 1. furthermore, by usingsome block operator matrix techniques, we nd explicit solution of the operator equationtxs*- sx*t*= a.

This paper deals with the existence of various types dual generalized inverses matrices. New and foundational results on necessary sufficient conditions for to exist are obtained. It is shown that unlike real matrices, matrices may not have {1}-dual inverses. A condition a matrix inverse always has {1}-, {1,3}-, {1,4}-, {1,2,3}-, {1,2,4}-dual if only it every {2}- {2,4}-dual inverse. Explicit e...