Weighted Moore-Penrose Inverse Research Articles

Recurrent neural networks for computing weighted Moore–Penrose inverse

Three recurrent neural networks are presented for computing the weighted Moore–Penrose inverse of rank-deficient matrices. The first recurrent neural network has the dynamical equation similar to the one proposed earlier for matrix inversion and is capable of weighted Moore–Penrose inverse under the condition of zero initial states. The second recurrent neural network consists of an array of neurons corresponding to a weighted Moore–Penrose inverse matrix with decaying self-connections and constant connections in each row or column. The third recurrent neural network consists of two layers of neuron arrays corresponding, respectively, to a weighted Moore–Penrose inverse and a Lagrangian matrix with constant connections.

Expression for the perturbation of the weighted Moore-Penrose inverse

We consider the perturbation formula for the weighted Moore-Penrose inverse of a rectangular matrix and give an explicit expression for the weighted Moore-Penrose inverse of a perturbed matrix under the weakest rank condition. This explicit expression extends the earlier work of several authors.

Universal Iterative Methods for Computing Generalized Inverses

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 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-Penrose inverse or to the group inverse. A few error estimates are derived. The advantages of the introduced methods over Tanabe's method [16] for computing reflexive generalized inverses are also investigated.

Weighted Moore-Penrose inverse of a boolean matrix

If A is a boolean matrix, then the weighted Moore-Penrose inverse of A (with respect to the given matrices M, N) is a matrix G which satisfies AGA = A, GAG = G, and that MAG and GAN are symmetric. Under certain conditions on M, N it is shown that the weighted Moore-Penrose inverse exists if and only if ANA T MA = A, in which case the inverse is N T A T M T . When M, N are identity matrices, this reduces to the well-known result that the Moore-Penrose inverse of a boolean matrix, when it exists, must be A T .

Weighted moore-penrose, Drazin, and group inverses of the Kronecker product A ⊗ B, and some applications

The representations for the weighted Moore-Penrose inverse, the Drazin inverse, and the group inverse of the Kronecker product A ⊗ B of the two matrices A and B are given, and by using these results, the determinant forms for projectors AA + MN , A + MN A, A d A, and A g A are deduced.

A finite algorithm for computing the weighted Moore-Penrose inverse A+MN

This paper presents a finite algorithm for computing the weighted Moore-Penrose inverse of a rectangular matrix. This algorithm may be viewed as an extension of Decell's algorithm.