364 citations · 576 across the 22 of their papers we have counts for
30 papers
Convergence and acceleration of a nonlinear fixed-point iteration for computing the Fitness Centrality of general graphs
Nikita Deniskin, Michele Benzi
We establish the global convergence of the (non-homogeneous) Fitness Centrality algorithm for general graphs, deriving an explicit convergence bound for the corresponding fixed-poi…
An augmented Lagrangian-based preconditioning technique for a class of block three-by-three linear systems
Fatemeh P. A. Beik, Michele Benzi
We propose an augmented Lagrangian-based preconditioner to accelerate the convergence of Krylov subspace methods applied to linear systems of equations with a block three-by-three…
Accelerating iterative solvers via a two-dimensional minimum residual technique
Fatemeh P. A. Beik, Michele Benzi, Mehdi Najafi-Kalyani
This paper deals with speeding up the convergence of a class of two-step iterative methods for solving linear systems of equations. To implement the acceleration technique, the res…
Computation of the von Neumann entropy of large matrices via trace estimators and rational Krylov methods
Michele Benzi, Michele Rinelli, Igor Simunec
We consider the problem of approximating the von Neumann entropy of a large, sparse, symmetric positive semidefinite matrix , defined as where $f(x)=-x…
Structural analysis of water networks
Michele Benzi, Isabella Daidone, Chiara Faccio +1
Liquid water, besides being fundamental for life on Earth, has long fascinated scientists due to several anomalies. Different hypotheses have been put forward to explain these pecu…
Efficient preconditioners for solving dynamical optimal transport via interior point methods
Enrico Facca, Gabriele Todeschi, Andrea Natale +1
In this paper we address the numerical solution of the quadratic optimal transport problem in its dynamical form, the so-called Benamou-Brenier formulation. When solved using inter…
Solving linear systems of the form by preconditioned iterative methods
Michele Benzi, Chiara Faccio
We consider the iterative solution of large linear systems of equations in which the coefficient matrix is the sum of two terms, a sparse matrix and a possibly dense, rank defi…
Solving cubic matrix equations arising in conservative dynamics
Michele Benzi, Milo Viviani
In this paper we consider the spatial semi-discretization of conservative PDEs. Such finite dimensional approximations of infinite dimensional dynamical systems can be described as…
New results and open problems on subgraph centrality
Nikita Deniskin, Michele Benzi
Subgraph centrality, introduced by Estrada and Rodríguez-Velázquez in [12], has become a widely used centrality measure in the analysis of networks, with applications in biology, n…
Low, high and very-high density forms of liquid water revealed by a medium-range order descriptor
Chiara Faccio, Michele Benzi, Laura Zanetti-Polzi +1
We present in this paper a computational approach based on molecular dynamics simulations and graph theory to characterize the structure of liquid water considering not only the lo…
Refined decay bounds on the entries of spectral projectors associated with sparse Hermitian matrices
Michele Benzi, Michele Rinelli
Spectral projectors of Hermitian matrices play a key role in many applications, and especially in electronic structure computations. Linear scaling methods for gapped systems are b…
Fully Atomistic Modeling of Realistic Plasmonic Materials: Assessing the Performance of Iterative Solvers
Piero Lafiosca, Tommaso Giovannini, Michele Benzi +1
The fully atomistic modeling of real-size plasmonic nanostructures is computationally demanding, therefore most calculations are limited to small-to-medium sized systems. However,…
Rational Krylov methods for fractional diffusion problems on graphs
Michele Benzi, Igor Simunec
In this paper we propose a method to compute the solution to the fractional diffusion equation on directed networks, which can be expressed in terms of the graph Laplacian as a…
Fast Iterative Solution of the Optimal Transport Problem on Graphs
Enrico Facca, Michele Benzi
In this paper, we address the numerical solution of the Optimal Transport Problem on undirected weighted graphs, taking the shortest path distance as transport cost. The optimal so…
Nonlocal network dynamics via fractional graph Laplacians
Michele Benzi, Daniele Bertaccini, Fabio Durastante +1
We introduce nonlocal dynamics on directed networks through the construction of a fractional version of a nonsymmetric Laplacian for weighted directed graphs. Furthermore, we provi…
Risk-dependent centrality in economic and financial networks
Paolo Bartesaghi, Michele Benzi, Gian Paolo Clemente +2
Node centrality is one of the most important and widely used concepts in the study of complex networks. Here, we extend the paradigm of node centrality in financial and economic ne…
What is the meaning of the graph energy after all?
Ernesto Estrada, Michele Benzi
For a simple graph with eigenvalues of the adjacency matrix , the energy of the graph is defined by . Myria…
Dynamic communicability and epidemic spread: a case study on an empirical dynamic contact network
Isabel Chen, Michele Benzi, Howard H. Chang +1
We analyze a recently proposed temporal centrality measure applied to an empirical network based on person-to-person contacts in an emergency department of a busy urban hospital. W…
Computation of generalized matrix functions
Francesca Arrigo, Michele Benzi, Caterina Fenu
We develop numerical algorithms for the efficient evaluation of quantities associated with generalized matrix functions [J. B. Hawkins and A. Ben-Israel, Linear and Multilinear Alg…
Core-satellite Graphs. Clustering, Assortativity and Spectral Properties
Ernesto Estrada, Michele Benzi
Core-satellite graphs (sometimes referred to as generalized friendship graphs) are an interesting class of graphs that generalize many well known types of graphs. In this paper we…
Edge modification criteria for enhancing the communicability of digraphs
Francesca Arrigo, Michele Benzi
We introduce new broadcast and receive communicability indices that can be used as global measures of how effectively information is spread in a directed network. Furthermore, we d…
Approximation of functions of large matrices with Kronecker structure
Michele Benzi, Valeria Simoncini
We consider the numerical approximation of where and is the sum of Kronecker products, that is ${\cal A}=M_2 \otimes I + I \otimes M_1…
Decay bounds for functions of matrices with banded or Kronecker structure
Michele Benzi, Valeria Simoncini
We present decay bounds for a broad class of Hermitian matrix functions where the matrix argument is banded or a Kronecker sum of banded matrices. Besides being significantly tight…
Updating and downdating techniques for optimizing network communicability
Francesca Arrigo, Michele Benzi
The total communicability of a network (or graph) is defined as the sum of the entries in the exponential of the adjacency matrix of the network, possibly normalized by the number…