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A Zeroing Neural Network Approach for Calculating Time-Varying G-Outer Inverse of Arbitrary Matrix [PDF]

IEEE Transactions on Neural Networks and Learning Systems
Calculation of the time-varying (TV) matrix generalized inverse has grown into an essential tool in many fields, such as computer science, physics, engineering, and mathematics, in order to tackle TV challenges.
Predrag S Stanimirović, Spyridon D Mourtas, Dijana Mosić   +2 more
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Characterizations of Outer Generalized Inverses

Canadian Mathematical Bulletin, 2017
AbstractLetRbe a ring andb,c∊R. In this paper, we give some characterizations of the (b,c)-inverse in terms of the direct sum decomposition, the annihilator, and the invertible elements. Moreover, elements with equal (b,c)-idempotents related to their (b,c)-inverses are characterized, and the reverse order rule for the (b,c)-inverse is considered.
Long Wang, Nieves Castro-Gonzalez, Jianlong Chen   +2 more
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Zeroing neural network approaches for computing time-varying minimal rank outer inverse [PDF]

Applied Mathematics and Computation
Generalized inverses are extremely effective in many areas of mathematics and engineering. The zeroing neural network (ZNN) technique, which is currently recognized as the state-of-the-art approach for calculating the time-varying Moore-Penrose matrix ...
Predrag S Stanimirović, Spyridon D Mourtas, Dijana Mosić   +2 more
exaly   +2 more sources

Outer generalized inverses in rings and related idempotents

Publicationes Mathematicae Debrecen, 2008
Summary: We investigate outer generalized inverses of elements in rings, and related idempotents. Among other things, if \(a'aa'=a'\) and \(b'bb'=b'\), we consider the relations \(b'b=a'a+u\) and \(bb'=aa'+v\) for a suitable choice of \(u\) and \(v\).
Načevska, Biljana, Djordjević, Dragan S.   +1 more
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Left and right G-outer inverses

Linear and Multilinear Algebra, 2020
The main contribution of this paper is to present new generalized inverses as weaker versions of a G-outer inverse.
Dijana Mosić, Long Wang
openaire   +1 more source

Determinantal Representation of Outer Inverses in Riemannian Space

Algebra Colloquium, 2012
Starting from a known determinantal representation of outer inverses, we derive their determinantal representation in terms of the inner product in the Euclidean space. We define the double inner product of two miscellaneous tensors of rank 2 in a Riemannian space.
Stanimirović, Predrag S., Zlatanović, Milan Lj.   +1 more
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The representation and approximations of outer generalized inverses

Acta Mathematica Hungarica, 2004
Let \(X\) and \(Y\) be Banach spaces, and \(A\in L(X,Y)\). An operator \(G\in L(X,Y)\) is called an outer generalized inverse \((OGI)\) of \(A\) if \(GAG=G\). A unified representation theorem for the class of all \(OGI\)'s of an operator is presented. The theorem is a generalization for the corresponding representation of the Moore-Penrose inverse [see
Djordjević, D. S., Stanimirović, P. S., Wei, Y.   +2 more
openaire   +1 more source

Composite outer inverses for rectangular matrices

Quaestiones Mathematicae, 2019
Various compositions of the Drazin inverse, the group inverse or the core-EP inverse with the Moore-Penrose inverse have investigated last years.
Dijana Mosić, Predrag S. Stanimirović
openaire   +1 more source

Sum of outer products dictionary learning for inverse problems

2016 IEEE Global Conference on Signal and Information Processing (GlobalSIP), 2016
The data-driven adaptation of synthesis dictionaries has been exploited in many applications in signal processing and imaging. This paper exploits efficient methods for aggregate sparsity penalized dictionary learning by first approximating the matrix of image patches with a sum of sparse rank-one matrices (outer products) and then using a block ...
Saiprasad Ravishankar, Raj Rao Nadakuditi, Jeffrey A. Fessler   +2 more
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Successive matrix squaring algorithm for computing outer inverses

Applied Mathematics and Computation, 2008
The authors derive a successive matrix squaring algorithm to approximate an outer generalized inverse with prescribed range and null space of a given matrix \(A \in \mathbb{C}_{r}^{m\times n}\). They propose an algorithm for computing various classes of outer generalized inverses of \(A\). Numerical examples are also provided.
Predrag S. Stanimirovic, Dragana S. Cvetkovic-Ilic   +1 more
openaire   +1 more source