In the last decades the Moore-Penrose pseudoinverse has found a wide range of applications in many areas of Science and became a useful tool for different scientists dealing with optimization problems, data analysis, solutions of linear integral equations, etc. At first we will present a review of some of the basic results on the so-called Moore-Penrose pseudoinverse of matrices, a concept that...

We introduce a generalized version of the Jang equation, designed for the general case of the Penrose Inequality in the setting of an asymptotically flat space-like hypersurface of a spacetime satisfying the dominant energy condition. The appropriate existence and regularity results are established in the special case of spherically symmetric Cauchy data, and are applied to give a new proof of ...

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...

In this paper we study an initial{boundary value Stefan{type problem with phase relaxation where the heat ux is proportional to the gradient of the inverse absolute temperature. This problem arises naturally as limiting case of the Penrose{Fife model for diiusive phase transitions with non{conserved order parameter if the coeecient of the interfacial energy is taken as zero. It is shown that th...

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...

We investigate the generalized Drazin inverse and the generalized resolvent in Banach algebras. The Laurent expansion of the generalized resolvent in Banach algebras is introduced. The Drazin index of a Banach algebra element is characterized in terms of the existence of a particularly chosen limit process. As an application, the computing of the Moore-Penrose inverse in C∗-algebras is consider...