A new Schulz-type method to compute the Moore-Penrose inverse of a matrix is proposed. Every iteration of the method involves four matrix multiplications. It is proved that this method converge with fourth-order. A wide set of numerical comparisons shows that the average number of matrix multiplications and the average CPU time of our method are considerably less than those of other methods.

The purpose of this paper is to investigate solvability systems constrained matrix equations in the form minimization problems. main novelty unification solutions considered with corresponding For a particular case we extend some well-known results and give several new for weak Drazin inverse. characterizations inverse, group inverse Moore–Penrose are obtained as consequences.

In this paper, we investigate the Sherman-Morrison-Woodbury formula for {1}-inverses and {2}-inverses of bounded linear operators on a Hilbert space. Some conditions are established to guarantee that (A+YGZ*)? = A? ?A?Y(G? +Z*A?Y)?Z*A? holds, where stands any kind standard inverse, {1}-inverse, {2}-inverse, Moore-Penrose Drazin group core inverse dual A.

An algorithm for computing {2, 3}, {2, 4}, {1, 2, 3}, {1, 2, 4}-inverses and the Moore-Penrose inverse of a given rational matrix A is established. Classes A{2, 3}s and A{2, 4}s are characterized in terms of matrix products (R∗A)†R∗ and T ∗(AT ∗)†, where R and T are rational matrices with appropriate dimensions and corresponding rank. The proposed algorithm is based on these general representat...

The Radon transform on Zn averages a function over its values on a translate of a fixed subset S in Zn. We discuss invertibility conditions and computer inverse formulas based on the Moore–Penrose inverse and on linear algorithms. We expect the results to be of use in directional and toroidal time series.

In this paper, it is given equivalent conditions for the absorption laws in terms of the Moore-Penrose, group, core inverse, core inverse dual, {1}, {1,2}, {1,3}, and {1,4} inverses in rings. The results given here extend the results of [X. Liu, H. Jin, and D.S. Cvetković-Ilić. The absorption laws for the generalized inverses. Appl. Math. Comp., 219:2053–2059, 2012.].

This paper extends some results for the weighted Moore–Penrose inverse A+M,N in Hilbert space to the so-called weighted Minkowski inverse A⊕M,N of an arbitrary rectangular matrix A ∈ Mm,n in Minkowski spaces μ. Four methods are also used for approximating the weighted Minkowski Inverse A⊕M,N . These methods are: Borel summable, Euler–Knopp summable, Newton–Raphson and Tikhonov’s methods. c © 20...

In this paper, we develop conditions under which the Sherman–Morrison–Woodbury formula can be represented in the Moore–Penrose inverse and the generalized Drazin inverse forms. These results generalize the original Sherman–Morrison–Woodbury formula. © 2011 Elsevier Ltd. All rights reserved.

The Radon transform on Zn averages a function over its values on a translate of a fixed subset S in Zn. We discuss invertibility conditions and computer inverse formulas based on the Moore-Penrose inverse and on linear algorithms. We expect the results to be of use in directional and toroidal time series.