22 citations · 68 across the 21 of their papers we have counts for
24 papers
Averaged Nyström interpolants for the solution of Fredholm integral equations of the second kind
Luisa Fermo, Lothar Reichel, Giuseppe Rodriguez +1
Fredholm integral equations of the second kind that are defined on a finite or infinite interval arise in many applications. This paper discusses Nyström methods based on Gauss qua…
Spectral computation with third-order tensors using the t-product
Anas El Hachimi, Khalide Jbilou, Ahmed Ratnani +1
The tensor t-product, introduced by Kilmer and Martin [26], is a powerful tool for the analysis of and computation with third-order tensors. This paper introduces eigentubes and ei…
A tensor bidiagonalization method for higher-order singular value decomposition with applications
Anas El Hachimi, Khalide Jbilou, Ahmed Ratnani +1
The need to know a few singular triplets associated with the largest singular values of third-order tensors arises in data compression and extraction. This paper describes a new me…
Perron communicability and sensitivity of multilayer networks
Smahane El-Halouy, Silvia Noschese, Lothar Reichel
Modeling complex systems that consist of different types of objects leads to multilayer networks, where nodes in the different layers represent different kind of objects. Nodes are…
On the banded Toeplitz structured distance to symmetric positive semidefiniteness
Silvia Noschese, Lothar Reichel
This paper is concerned with the determination of a close real banded positive definite Toeplitz matrix in the Frobenius norm to a given square real banded matrix. While it is stra…
Adaptive cross approximation for Tikhonov regularization in general form
Thomas Mach, Lothar Reichel, Marc Van Barel
Many problems in Science and Engineering give rise to linear integral equations of the first kind with a smooth kernel. Discretization of the integral operator yields a matrix, who…
Tensor regularization by truncated iteration: a comparison of some solution methods for large-scale linear discrete ill-posed problem with a t-product
Ugochukwu O. Ugwu, Lothar Reichel
This paper describes and compares some structure preserving techniques for the solution of linear discrete ill-posed problems with the t-product. A new randomized tensor singular v…
Tensor Arnoldi-Tikhonov and GMRES-type methods for ill-posed problems with a t-product structure
Lothar Reichel, Ugochukwu O. Ugwu
This paper describes solution methods for linear discrete ill-posed problems defined by third order tensors and the t-product formalism introduced in [M. E. Kilmer and C. D. Martin…
Weighted tensor Golub-Kahan-Tikhonov-type methods applied to image processing using a t-product
Lothar Reichel, Ugochukwu O Ugwu
This paper discusses weighted tensor Golub-Kahan-type bidiagonalization processes using the t-product. This product was introduced in [M. E. Kilmer and C. D. Martin, Factorization…
Communication in Complex Networks
Omar De la Cruz Cabrera, Jiafeng Jin, Silvia Noschese +1
One of the properties of interest in the analysis of networks is \emph{global communicability}, i.e., how easy or difficult it is, generally, to reach nodes from other nodes by fol…
Estimating and increasing the structural robustness of a network
Silvia Noschese, Lothar Reichel
The capability of a network to cope with threats and survive attacks is referred to as its robustness. This paper discusses one kind of robustness, commonly denoted structural robu…
Continuous Adaptive Cross Approximation for Ill-posed Problems with Chebfun
Abdulaziz Alqahtani, Thomas Mach, Lothar Reichel
The analysis of linear ill-posed problems often is carried out in function spaces using tools from functional analysis. However, the numerical solution of these problems typically…
Functions and eigenvectors of partially known matrices with applications to network analysis
Mohammed Al Mugahwi, Omar De la Cruz Cabrera, Silvia Noschese +1
Matrix functions play an important role in applied mathematics. In network analysis, in particular, the exponential of the adjacency matrix associated with a network provides valua…
On the Golub--Kahan bidiagonalization for ill-posed tensor equations with applications to color image restoration
Fatemeh P. A. Beik, Khalide Jbilou, Mehdi Najafi-Kalyani +1
This paper is concerned with solving ill-posed tensor linear equations. These kinds of equations may appear from finite difference discretization of high-dimensional convection-dif…
Error Estimates for Arnoldo-Tikhonov Regularization for Ill-Posed Operator Equations
Ronny Ramlau, Lothar Reichel
Most of the literature on the solution of linear ill-posed operator equations, or their discretization, focuses only on the infinite-dimensional setting or only on the solution of…
A spectral method for bipartizing a network and detecting a large anti-community
A. Concas, S. Noschese, L. Reichel +1
Relations between discrete quantities such as people, genes, or streets can be described by networks, which consist of nodes that are connected by edges. Network analysis aims to i…
Eigenvector sensitivity under general and structured perturbations of tridiagonal Toeplitz-type matrices
Silvia Noschese, Lothar Reichel
The sensitivity of eigenvalues of structured matrices under general or structured perturbations of the matrix entries has been thoroughly studied in the literature. Error bounds ar…
Arnoldi decomposition, GMRES, and preconditioning for linear discrete ill-posed problems
Silvia Gazzola, Silvia Noschese, Paolo Novati +1
GMRES is one of the most popular iterative methods for the solution of large linear systems of equations that arise from the discretization of linear well-posed problems, such as D…
Regularization matrices for discrete ill-posed problems in several space-dimensions
Laura Dykes, Guangxin Huang, Silvia Noschese +1
Many applications in science and engineering require the solution of large linear discrete ill-posed problems that are obtained by the discretization of a Fredholm integral equatio…
Computing Unstructured and Structured Polynomial Pseudospectrum Approximations
Silvia Noschese, Lothar Reichel
In many applications it is important to understand the sensitivity of eigenvalues of a matrix polynomial to perturbations of the polynomial. The sensitivity commonly is described b…
Approximated structured pseudospectra
Silvia Noschese, Lothar Reichel
Pseudospectra and structured pseudospectra are important tools for the analysis of matrices. Their computation, however, can be very demanding for all but small matrices. A new app…
Circulant preconditioners for discrete ill-posed Toeplitz systems
L. Dykes, S. Noschese, L. Reichel
Circulant preconditioners are commonly used to accelerate the rate of convergence of iterative methods when solving linear systems of equations with a Toeplitz matrix. Block extens…
Regularization matrices determined by matrix nearness problems
Guangxin Huang, Silvia Noschese, Lothar Reichel
This paper is concerned with the solution of large-scale linear discrete ill-posed problems with error-contaminated data. Tikhonov regularization is a popular approach to determine…
Some matrix nearness problems suggested by Tikhonov regularization
Silvia Noschese, Lothar Reichel
The numerical solution of linear discrete ill-posed problems typically requires regularization, i.e., replacement of the available ill-conditioned problem by a nearby better condit…