In this paper, we import interval method to the iteration for computing Moore-Penrose inverse of the full row (or column) rank matrix. Through modifying the classical Newton iteration by interval method, we can get better numerical results. The convergence of the interval iteration is proven. We also give some numerical examples to compare interval iteration with classical Newton iteration.

In this paper, we study the Moore-Penrose inverse of a symmetric rank-one perturbed matrix from which a finite method is proposed for the minimum-norm least-squares solution to the system of linear equations Ax = b. This method is guaranteed to produce the required result.

Utilizing the Moore-Penrose generalized inverse of the Jacobian matrix of wire-actuated parallel robot manipulators, one or more wire tensions could be negative. In this paper, a methodology for calculating positive wire tensions, with minimum 2-norm for tension vector, is presented. A planar parallel manipulator is simulated to illustrate the proposed methodology.

We analyze when the Moore–Penrose inverse of the combinatorial Laplacian of a distance– regular graph is a M–matrix; that is, it has non–positive off–diagonal elements. In particular, our results include some previously known results on strongly regular graphs.

In this paper, we study the Moore-Penrose inverse of a symmetric rank-one perturbed matrix from which a finite method is proposed for the minimum-norm least-squares solution to the system of linear equations Ax = b. This method is guaranteed to produce the required result.

We prove some identities related to the reverse order law for the Moore-Penrose inverse of operators on Hilbert spaces, extending some results from (Y. Tian and S. Cheng, Linear Multilinear Algebra 52 (2004)) and (R. E. Cline, SIAM Review, Vol. 6, No. 1 (1964)) to infinite dimensional settings. 2010 Mathematics Subject Classification: 47A05, 15A09.

Let A be a nonnegative idempotent matrix. It is shown that the Schur complement of a submatrix, using the Moore-Penrose inverse, is a nonnegative idempotent matrix if the submatrix has a positive diagonal. Similar results for the Schur complement of any submatrix of A are no longer true in general.

In this paper, using some block-operator matrix techniques, we give the necessary and sufficient conditions for the reverse order law for {1, 2, 3} and {1, 2, 4}−inverses of bounded operators on Hilbert spaces. Furthermore, we present new equivalent conditions for the reverse order law for the Moore-Penrose inverse. AMS classification: 15A09

By using the complex representation of quaternion matrices, the Moore–Penrose generalized inverse and the Kronecker product of matrices, the expressions of the least squares η-Hermitian solution with the least norm and the expressions of the least squares η-anti-Hermitian solution with the least norm are derived for the matrix equation AXB+CXD = E over quaternions.

There are three weighted decompositions of tensors proposed in this paper, and the corresponding definitions generalized tensor functions given. The Cauchy integral formula Moore-Penrose inverse is developed for solving equations. Besides above, we give projection to discuss representations power tensors. Finally, some special studied which can preserve structural invariance under defined paper.