This paper presents a fast computational method that finds application in a broad scientific field such as digital image restoration. The proposed method provides a new approach to the problem of image reconstruction by using the Moore-Penrose inverse. The resolution of the reconstructed image remains at a very high level but the main advantage of the method was found on the computational load ...

Fuglede-Putnam theorem is not true in general for $ EP operators on Hilbert spaces. We prove that under some conditions the holds good. If adjoint operation replaced by Moore-Penrose inverse theorem, we get type -- however proofs are totally different. Finally, interesting results have been proved using several versions of theorems

In this paper, we investigate the least squares solution with minimal norm to system (1.1) over reduced biquaternion via complex representation of tensors and Moore–Penrose inverse tensors. Besides, establish some necessary sufficient conditions for solvability above give an expression general when are met. Moreover, algorithm numerical example presented verify main results paper.

A new characterization of row-monotone matrices is given and is related to the Moore-Penrose generalized inverse. The M-matrix concept is extended to rectangular matrices with full column rank. A structure theorem is provided for all matrices A with full column rank for which the generalized inverse A+ & 0. These results are then used to investigate convergent splittings of rectangular matrices...

By using Moore-Penrose generalized inverse and the general singular value decomposition of matrices, this paper establishes the necessary and sufficient conditions for the existence of and the expressions for the centrosymmetric solutions with a submatrix constraint of matrix inverse problem AX = B. In addition, in the solution set of corresponding problem, the expression of the optimal approxi...

In this article we consider the system of operator equations T_iX=U_i for i=1,2,...,n and give necessary and suffcient conditions for the existence of common Hermitian solutions to this system of operator equations for arbitrary operators without the closedness condition. Also we study the Moore-penrose inverse of a ncross 1 block operator matrix and. then gi...