Related papers: Generalized Inversion of Nonlinear Operators

Line graphs are an alternative representation of graphs where each vertex of the original (root) graph becomes an edge. However not all graphs have a corresponding root graph, hence the transformation from graphs to line graphs is not…

Unfolding problems often arise in the context of statistical data analysis. Such problematics occur when the probability distribution of a physical quantity is to be measured, but it is randomized (smeared) by some well understood process,…

Using the recent notion of inverse along an element in a semigroup, and the natural partial order on idempotents, we study bicommuting generalized inverses and define a new inverse called natural inverse, that generalizes the Drazin inverse…

Convolutional Neural Networks (CNNs) have become the state-of-the-art in supervised learning vision tasks. Their convolutional filters are of paramount importance for they allow to learn patterns while disregarding their locations in input…

The aim of this paper is to introduce and study left and right versions of the class of generalized Drazin-Riesz invertible operators, as well as left and right versions of the class of generalized Drazin-meromorphic invertible operators.

The article presents a matrix differential operator and a pseudoinverse matrix differential operator for finding a particular solution to nonhomogeneous linear ordinary differential equations (ODE) with constant coefficients with special…

Standard neural networks can approximate general nonlinear operators, represented either explicitly by a combination of mathematical operators, e.g., in an advection-diffusion-reaction partial differential equation, or simply as a black…

The Moore-Penrose inverse is a genuine extension of the matrix inverse. Given a complex matrix, there uniquely exists another complex matrix satisfying the four Moore-Penrose conditions, and if the original matrix is nonsingular, it is…

In this paper, we provide a few properties of the weighted Moore--Penrose inverse for an arbitrary order tensor via the Einstein product. We again obtain some new sufficient conditions for the reverse-order law of the weighted…

Under consideration are mathematical models of heat and mass transfer. We study inverse problems of recovering lower-order coefficients in a second order parabolic equation. The coefficients are representable in the form of a finite…

There has been proposed a new method of the constructing of the basic functions for spaces of tensor representations of the Lie groups with the help of the generalized Casimir operator. In the definition of the operator there were used the…

The convergence of a new general variable metric algorithm based on compositions of averaged operators is established. Applications to monotone operator splitting are presented.

All one-condition generalized inverses of the Markovian kernel I - P, where P is the transition matrix of a finite irreducible Markov chain, can be uniquely specified in terms of the stationary probabilities and the mean first passage times…

In the last decades many authors have become interested in the study of multilinear and polynomial generalizations of families of operator ideals (such as, for instance, the ideal of absolutely summing operators). However, these…

Neural operators, which emerge as implicit solution operators of hidden governing equations, have recently become popular tools for learning responses of complex real-world physical systems. Nevertheless, the majority of neural operator…

We study two nonlinear methods for statistical linear inverse problems when the operator is not known. The two constructions combine Galerkin regularization and wavelet thresholding. Their performances depend on the underlying structure of…

Can regularization terms in the training of invertible neural networks lead to known Bayesian point estimators in reconstruction? Invertible networks are attractive for inverse problems due to their inherent stability and interpretability.…

Divergences are quantities that measure discrepancy between two probability distributions and play an important role in various fields such as statistics and machine learning. Divergences are non-negative and are equal to zero if and only…

Learned image reconstruction has become a pillar in computational imaging and inverse problems. Among the most successful approaches are learned iterative networks, which are formulated by unrolling classical iterative optimisation…

Inverse problems arise anywhere we have indirect measurement. As, in general they are ill-posed, to obtain satisfactory solutions for them needs prior knowledge. Classically, different regularization methods and Bayesian inference based…