Results 101 to 110 of about 4,185 (184)

A characterization of the Moore-Penrose inverse

, 1993
If A is a nonsingular matrix of order n, the inverse of A is the unique matrix X for which rankAIIX=rank(A). We present a generalization of this fact to singular or rectangular matrices A to obtain an analogous result for the Moore-Penrose inverse A+ of ...
Markham, Thomas L., Fiedler, Miroslav
core   +1 more source

ON THE MEAN AND DISPERSION OF THE MOORE-PENROSE GENERALIZED INVERSE OF A WISHART MATRIX

, 2020
The Moore-Penrose inverse of a singular Wishart matrix is studied. When the scale matrix equals the identity matrix the mean and dispersion matrices of the Moore-Penrose inverse are known. When the scale matrix has an arbitrary structure no exact results
von Rosen, Dietrich, Imori, Shinpei, Imori, Shinpei,, von Rosen, Dietrich,   +3 more
core   +1 more source

Optimizing the ordering of the Hadamard masks of ghost imaging suitable for the efficient face reconstruction using the max-projection method. [PDF]

Sci Rep, 2023
Zhang H, Du K, Zhao C, Tang J, Si S, Jia W, Xue L, Li Z.   +7 more
europepmc   +1 more source

Complex degenerate metrics in general relativity: a covariant extension of the Moore–Penrose algorithm

European Physical Journal C: Particles and Fields
The Moore–Penrose algorithm provides a generalized notion of an inverse, applicable to degenerate matrices. In this paper, we introduce a covariant extension of the Moore–Penrose method that permits to deal with general relativity involving complex non ...
Arthur Garnier, Emmanuele Battista
doaj   +1 more source

INTERVAL ITERATIVE METHODS FOR COMPUTING MOORE-PENROSE INVERSE ∗

, 2008
In this paper, we import interval method to the iteration for computing Moore-Penrose inverse of the full row (or column) rank matrix. Through modifying the classical Newton iteration by interval method, we can get better numerical results.
Xian Zhang, Yimin Wei, Jianfeng Cai
core  

Dykstra's Algorithm and a Representation of the Moore–Penrose Inverse

, 2002
The convergence of Lardy's series representation of the Moore–Penrose inverse of a closed unbounded linear operator is proved via Dykstra's alternating projection ...
Groetsch, C.W.
core   +1 more source

A Review on Large-Scale Data Processing with Parallel and Distributed Randomized Extreme Learning Machine Neural Networks

Mathematical and Computational Applications
The randomization-based feedforward neural network has raised great interest in the scientific community due to its simplicity, training speed, and accuracy comparable to traditional learning algorithms.
Elkin Gelvez-Almeida, Marco Mora, Ricardo J. Barrientos, Ruber Hernández-García, Karina Vilches-Ponce, Miguel Vera   +5 more
doaj   +1 more source

Existence Criteria and Related Relation of the gMP Inverse of Matrices

Mathematics
New characterizations of the gMP inverse are provided by the core part of the core-EP decomposition. We also answer the question as to whether X is the gMP inverse of A under the conditions of R(X)⊆R(A*Ak) or N((Ak)*)⊆N(X).
Sanzhang Xu, Honglin Zou, Kezheng Zuo
doaj   +1 more source

A note on the convexity of the Moore–Penrose inverse

, 2018
This note is a sequel to an earlier study (Nordström [7]) on convexity properties of the inverse and Moore–Penrose inverse, in which the following question was raised.
Kenneth, Nordström, Nordström, Kenneth
core   +1 more source

Perturbation results and the forward order law for the Moore-Penrose inverse of a product

, 2018
New expressions are given for the Moore-Penrose inverse of a product $AB$ of two complex matrices. Furthermore, an expression for $(AB)\dg - B\dg A\dg$ for the case where $A$ or $B$ is of full rank is provided. Necessary and sufficient conditions for the
Castro-Gonzalez, Nieves, Hartwig, Robert
core   +1 more source