142 citations · 303 across the 24 of their papers we have counts for
29 papers
Robust forms for passive descriptor systems
Peter Benner, Anshul Prajapati, Paul Van Dooren
We show how to compute the passivity radius of a given generalized state-space model of a rational transfer function that represents a passive system, both in the continuous-time a…
Para-Hermitian rational matrices
Froilán Dopico, Vanni Noferini, María C. Quintana +1
In this paper we study para-Hermitian rational matrices and the associated structured rational eigenvalue problem (REP). Para-Hermitian rational matrices are square rational matric…
A MATLAB package computing simultaneous Gaussian quadrature rules for Multiple Orthogonal Polynomials
Teresa Laudadio, Nicola Mastronardi, Walter Van Assche +1
The aim of this paper is to describe a Matlab package for computing the simultaneous Gaussian quadrature rules associated with a variety of multiple orthogonal polynomials. Multipl…
Assigning Stationary Distributions to Sparse Stochastic Matrices
Nicolas Gillis, Paul Van Dooren
The target stationary distribution problem (TSDP) is the following: given an irreducible stochastic matrix and a target stationary distribution , construct a minimum no…
Minimal rank factorizations of polynomial matrices
Andrii Dmytryshyn, Froilán Dopico, Paul Van Dooren
We investigate rank revealing factorizations of polynomial matrices into products of three, , or two, , polynomial matr…
Parameterized Interpolation of Passive Systems
Peter Benner, Pawan Goyal, Paul Van Dooren
We study the tangential interpolation problem for a passive transfer function in standard state-space form. We derive new interpolation conditions based on the computation of a def…
Computing a compact local Smith McMillan form
Vanni Noferini, Paul Van Dooren
We define a compact local Smith-McMillan form of a rational matrix as the diagonal matrix whose diagonal elements are the nonzero entries of a local Smith-McMillan form of $…
A Riemannian Optimization Approach to Clustering Problems
Wen Huang, Meng Wei, Kyle A. Gallivan +1
This paper considers the optimization problem in the form of where is smooth, $\mathcal{F}_v = \{X \in \mathbb{R}^{n \times q} : X…
Root vectors of polynomial and rational matrices: theory and computation
Vanni Noferini, Paul Van Dooren
The notion of root polynomials of a polynomial matrix was thoroughly studied in [F. Dopico and V. Noferini, Root polynomials and their role in the theory of matrix polynomia…
On computing root polynomials and minimal bases of matrix pencils
Vanni Noferini, Paul Van Dooren
We revisit the notion of root polynomials, thoroughly studied in [F. Dopico and V. Noferini, Root polynomials and their role in the theory of matrix polynomials, Linear Algebra App…
Root-max Problems, Hybrid Expansion-Contraction, and Quadratically Convergent Optimization of Passive Systems
Tim Mitchell, Paul Van Dooren
We present quadratically convergent algorithms to compute the extremal value of a real parameter for which a given rational transfer function of a linear time-invariant system is p…
Structural backward stability in rational eigenvalue problems solved via block Kronecker linearizations
Froilán M. Dopico, María C. Quintana, Paul Van Dooren
We study the backward stability of running a backward stable eigenstructure solver on a pencil that is a strong linearization of a rational matrix expressed in the fo…
Diagonal scalings for the eigenstructure of arbitrary pencils
Froilán M. Dopico, María C. Quintana, Paul Van Dooren
In this paper we show how to construct diagonal scalings for arbitrary matrix pencils , in which both and are complex matrices (square or nonsquare). The goal of such…
Optimal robustness of port-Hamiltonian systems
Volker Mehrmann, Paul Van Dooren
We construct optimally robust port-Hamiltonian realizations of a given rational transfer function that represents a passive system. We show that the realization with a maximal pass…
Block minimal bases -ifications of matrix polynomials
Froilán M. Dopico, Javier Pérez, Paul Van Dooren
The standard way of solving a polynomial eigenvalue problem associated with a matrix polynomial starts by embedding the matrix coefficients of the polynomial into a matrix pencil,…
Robustness and perturbations of minimal bases II: The case with given row degrees
Froilán M. Dopico, Paul Van Dooren
This paper studies generic and perturbation properties inside the linear space of polynomial matrices whose rows have degrees bounded by a given list $d_1, \ldots,…
Block Kronecker Linearizations of Matrix Polynomials and their Backward Errors
Froilán M. Dopico, Piers W. Lawrence, Javier Pérez +1
We introduce a new family of strong linearizations of matrix polynomials---which we call "block Kronecker pencils"---and perform a backward stability analysis of complete polynomia…
Structured backward error analysis of linearized structured polynomial eigenvalue problems
Froilán M. Dopico, Javier Pérez, Paul Van Dooren
We introduce a new class of structured matrix polynomials, namely, the class of M_A-structured matrix polynomials, to provide a common framework for many classes of structured matr…
Robustness and Perturbations of Minimal Bases
Paul Van Dooren, Froilán M. Dopico
Polynomial minimal bases of rational vector subspaces are a classical concept that plays an important role in control theory, linear systems theory, and coding theory. It is a comm…
Sparse matrix factorizations for fast linear solvers with application to Laplacian systems
Michael T. Schaub, Maguy Trefois, Paul Van Dooren +1
In solving a linear system with iterative methods, one is usually confronted with the dilemma of having to choose between cheap, inefficient iterates over sparse search directions…
A framework for structured linearizations of matrix polynomials in various bases
Leonardo Robol, Raf Vandebril, Paul Van Dooren
We present a framework for the construction of linearizations for scalar and matrix polynomials based on dual bases which, in the case of orthogonal polynomials, can be described b…
Low-rank Similarity Measure for Role Model Extraction
Arnaud Browet, Paul Van Dooren
Computing meaningful clusters of nodes is crucial to analyze large networks. In this paper, we present a pairwise node similarity measure that allows to extract roles, i.e. group o…
Fast community detection using local neighbourhood search
Arnaud Browet, P. -A. Absil, Paul Van Dooren
Communities play a crucial role to describe and analyse modern networks. However, the size of those networks has grown tremendously with the increase of computational power and dat…
Significant Scales in Community Structure
V. A. Traag, G. Krings, P. Van Dooren
Many complex networks show signs of modular structure, uncovered by community detection. Although many methods succeed in revealing various partitions, it remains difficult to dete…