About the generalized LM-inverse and the weighted Moore–Penrose inverse

Abstract

The recursive method for computing the generalized LM -inverse of a constant rectangular matrix augmented by a column vector is proposed in [16,17]. The corresponding algorithm for the sequential determination of the generalized LM -inverse is established in the present paper. We prove that the introduced algorithm for computing the generalized LM inverse and the algorithm for the computation of the weighted Moore-Penrose inverse developed by Wang in [23] are equivalent algorithms. Both of the algorithms are implemented in the present paper using the package MATHEMATICA. Several rational test matrices and randomly generated constant matrices are tested and the CPU time is compared and discussed.

Weighted Moore–Penrose generalized matrix inverse: MySQL vs. Cassandra database storage system

“…In our previous article we presented the implementation of the weighted Moore-Penrose inverse by procedural programming approach in PHP and MySQL database [1]. Previously, we have also stated the conditions which characterize the weighted Moore-Penrose inverse in our article [2]. Our main motivation was to provide better access compared to our previous work, as well as other studies, primarily in the field of matrix calculations.…”

“…Also, the research concerning the comparison of relation database system, MySQL and key value store system, Cassandra, on the database layer. In our article [2] we have stated the conditions which characterize the weighted Moore-Penrose inverse.…”

Computation of generalized inverses using PHP/MySQL environment

“…The algorithm is applied in order to develop the client/server Web application for computing the Moore-Penrose inverse, the weighted Moore-Penrose inverse as well as the fundamental matrix operations. Based on the analysis of available algorithms and our previous work in this area (see [17,18,19,20,22,21,23,24]), we have identified operations, which are useful for a number of similar algorithms.…”

On Convergents Infinite Products and Some Generalized Inverses of Matrix Sequences

“…Abstract and Applied Analysis Also, the representation and characterization for the outer generalized inverse A 2 T,S have been considered by many authors see, e.g., 15,16,20,27,30,31 Finally, given two matrices A a ij ∈ M m,n , and B b kl ∈ M p,q , then the Kronecker product of A and B is defined by see, e.g., 5, 7, 32-35…”