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Characterizations, iterative method, sign pattern and perturbation analysis for the DMP inverse with its applications. (English) Zbl 1488.65083

Summary: This paper is a study on main properties and characterizations of the DMP inverse. Also, corresponding representations and computational procedures are derived. Particularly, an upgrade of the bordering method to the case of the DMP inverse is considered as well as applications of the DMP inverse in solving singular linear systems. Also, the DMP inverse of an upper block triangular matrix and its sign pattern are investigated. Furthermore, several computational procedures aimed to approximating the DMP inverse are developed, implemented and tested. The main of them are the limit representation, a revised successive matrix squaring iterations and the Gradient Neural Network (GNN) dynamical system. Finally, some perturbation bounds and continuity of the DMP inverse are studied.

MSC:

65F20 Numerical solutions to overdetermined systems, pseudoinverses
15A10 Applications of generalized inverses
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