B. Meini

activity

20102026

most citedSemi-Infinite Quasi-Toeplitz Matrices with Applications to QBD Stochastic Processes

28 citations · 142 across the 24 of their papers we have counts for

collaborators

28 papers

math.NA2026

Component-wise accurate fixed point iterations for computing the square root of a singular M-matrix

Dario Andrea Bini, Bruno Iannazzo, Beatrice Meini +1

We analyze two fixed-point iterations for computing the principal square root of an M-matrix $A$ . Although these iterations, with customary initialization, converge sublinearly whe…

math.NA2026

Component-wise accurate computation of the square root of an M-matrix

Dario A. Bini, Bruno Iannazzo, Beatrice Meini +1

Component-wise accurate algorithms for computing the principal square root of an M-matrix are designed in terms of triplet representations. A triplet representation of an M-matrix…

math.NA2025

The Derivative of Kemeny's Constant as a Centrality Measure in Undirected Graphs

Dario A. Bini, Beatrice Meini, Federico Poloni

Kemeny's constant quantifies a graph's connectivity by measuring the average time for a random walker to reach any other vertex. We introduce two concepts of the directional deriva…

math.NA2024

Cut-edge centralities in an undirected graph

Dario Bini, Steve Kirkland, Guy Latouche +1

A centrality measure of the cut-edges of an undirected graph, given in [Altafini et al.~SIMAX 2023] and based on Kemeny's constant, is revisited. A numerically more stable expressi…

math.NA2024

On certain matrix algebras related to quasi-Toeplitz matrices

Dario Bini, Beatrice Meini

Let $A_{α}$ be the semi-infinite tridiagonal matrix having subdiagonal and superdiagonal unit entries, $(A_{α})_{11} = α$ , where $α \in C$ , and zero elsewhere. A basis $\{P_0,P_1,P…

math.NA2023★ 2 cited

On Kemeny's constant and stochastic complement

Dario Andrea Bini, Fabio Durastante, Sooyeong Kim +1

Given a stochastic matrix $P$ partitioned in four blocks $P_{ij}$ , $i, j = 1, 2$ , Kemeny's constant $κ (P)$ is expressed in terms of Kemeny's constants of the stochastic complements $P_…

math.NA2023

Invariant subspaces of $T$ -palindromic pencils and algebraic $T$ -Riccati equations

Bruno Iannazzo, Beatrice Meini, Federico Poloni

By exploiting the connection between solving algebraic $⊤$ -Riccati equations and computing certain deflating subspaces of $⊤$ -palindromic matrix pencils, we obtain theoretica…

math.NA2022

A defect-correction algorithm for quadratic matrix equations, with applications to quasi-Toeplitz matrices

Dario Bini, Beatrice Meini

A defect correction formula for quadratic matrix equations of the kind $A_{1} X^{2} + A_{0} X + A_{- 1} = 0$ is presented. This formula, expressed by means of an invariant subspace of a suitable…

math.NA2022

Relaxed Fixed Point Iterations for Matrix Equations Arising in Markov Chains Modeling

Luca Gemignani, Beatrice Meini

We present some accelerated variants of fixed point iterations for computing the minimal non-negative solution of the unilateral matrix equation associated with an M/G/1-type Marko…

math.NA2022★ 5 cited

Computing eigenvalues of semi-infinite quasi-Toeplitz matrices

D. A. Bini, B. Iannazzo, B. Meini +2

A quasi-Toeplitz (QT) matrix is a semi-infinite matrix of the form $A = T (a) + E$ where $T (a)$ is the Toeplitz matrix with entries $(T (a))_{i, j} = a_{j - i}$ , for $a_{j - i} \in C$ , $i…

math.NA2022

An edge centrality measure based on the Kemeny constant

D. Altafini, D. A. Bini, V. Cutini +2

A new measure $c (e)$ of the centrality of an edge $e$ in an undirected graph $G$ is introduced. It is based on the variation of the Kemeny constant of the graph after removing the…

math.NA2021

Palindromic linearization and numerical solution of nonsymmetric algebraic T-Riccati equations

Peter Benner, Bruno Iannazzo, Beatrice Meini +1

We identify a relationship between the solutions of a nonsymmetric algebraic T-Riccati equation (T-NARE) and the deflating subspaces of a palindromic matrix pencil, obtained by arr…

math.NA2021

Numerical solution of a matrix integral equation arising in Markov Modulated Lévy processes

Dario A. Bini, Guy Latouche, Beatrice Meini

Markov-modulated Lévy processes lead to matrix integral equations of the kind $A_{0} + A_{1} X + A_{2} X^{2} + A_{3} (X) = 0$ where $A_{0}$ , $A_{1}$ , $A_{2}$ are given matrix coefficients, while $A_{3} (X)$ …

math.NA2020

A family of fast fixed point iterations for M/G/1-type Markov chains

Dario Andrea Bini, Guy Latouche, Beatrice Meini

We consider the problem of computing the minimal nonnegative solution $G$ of the nonlinear matrix equation $X = \sum_{i = - 1}^{\infty} A_{i} X^{i + 1}$ where $A_{i}$ , for $i \geq - 1$ , are nonnega…

math.PR2019

Traffic lights, clumping and QBDs

Steven Finch, Guy Latouche, Guy Louchard +1

In discrete time, $ℓ$ -blocks of red lights are separated by $ℓ$ -blocks of green lights. Cars arrive at random. \ We seek the distribution of maximum line length of idle cars,…

math.NA2019★ 10 cited

A computational framework for two-dimensional random walks with restarts

Dario A. Bini, Stefano Massei, Beatrice Meini +1

The treatment of two-dimensional random walks in the quarter plane leads to Markov processes which involve semi-infinite matrices having Toeplitz or block Toeplitz structure plus a…

math.NA2019★ 15 cited

Solving quadratic matrix equations arising in random walks in the quarter plane

Dario A. Bini, Beatrice Meini, Jie Meng

Quadratic matrix equations of the kind $A_{1} X^{2} + A_{0} X + A_{- 1} = X$ are encountered in the analysis of Quasi--Birth-Death stochastic processes where the solution of interest is the minim…

math.PR2017

Why is Kemeny's constant a constant?

Dario Bini, Jeffrey J. Hunter, Guy Latouche +2

In their 1960 book on finite Markov chains, Kemeny and Snell established that a certain sum is invariant. The value of this sum has become known as {\it Kemeny's constant}. Various…

math.NA2017★ 19 cited

Perron-based algorithms for the multilinear pagerank

Beatrice Meini, Federico Poloni

We consider the multilinear pagerank problem studied in [Gleich, Lim and Yu, Multilinear Pagerank, 2015], which is a system of quadratic equations with stochasticity and nonnegativ…

math.NA2016★ 13 cited

On Functions of quasi Toeplitz matrices

Dario A. Bini, Stefano Massei, Beatrice Meini

Let $a (z) = \sum_{i \in Z} a_{i} z^{i}$ be a complex valued continuous function, defined for $∣ z ∣ = 1$ , such that $\sum_{i = - \infty}^{+ \infty} ∣ i a_{i} ∣ < \infty$ . Consider the semi-infinite…

math.NA2016★ 16 cited

On the exponential of semi-infinite quasi-Toeplitz matrices

Dario A. Bini, Beatrice Meini

Let $a (z) = \sum_{i \in Z} a_{i} z^{i}$ be a complex valued function defined for $∣ z ∣ = 1$ , such that $\sum_{i \in Z} ∣ i a_{i} ∣ < \infty$ , and let $E = (e_{i, j})_{i, j \in Z^{+}}$ b…

math.NA2016★ 28 cited

Semi-Infinite Quasi-Toeplitz Matrices with Applications to QBD Stochastic Processes

Dario A. Bini, Stefano Massei, Beatrice Meini

Denote by $W_{1}$ the set of complex valued functions of the form $a (z) = \sum_{i = - \infty}^{+ \infty} a_{i} z^{i}$ which are continuous on the unit circle, and such that $\sum_{i=-\…

math.NA2016★ 8 cited

General solution of the Poisson equation for Quasi-Birth-and-Death processes

Dario A. Bini, Sarah Dendievel, Guy Latouche +1

We consider the Poisson equation $(I - P) u = g$ , where $P$ is the transition matrix of a Quasi-Birth-and-Death (QBD) process with infinitely many levels, $\bm…

math.NA2016★ 4 cited

Shift techniques for Quasi-Birth and Death processes: canonical factorizations and matrix equations

Dario A. Bini, Guy Latouche, Beatrice Meini

We revisit the shift technique applied to Quasi-Birth and Death (QBD) processes (He, Meini, Rhee, SIAM J. Matrix Anal. Appl., 2001) by bringing the attention to the existence and p…

Component-wise accurate fixed point iterations for computing the square root of a singular M-matrix

Component-wise accurate computation of the square root of an M-matrix

The Derivative of Kemeny's Constant as a Centrality Measure in Undirected Graphs

Cut-edge centralities in an undirected graph

On certain matrix algebras related to quasi-Toeplitz matrices

On Kemeny's constant and stochastic complement

Invariant subspaces of T-palindromic pencils and algebraic T-Riccati equations

A defect-correction algorithm for quadratic matrix equations, with applications to quasi-Toeplitz matrices

Relaxed Fixed Point Iterations for Matrix Equations Arising in Markov Chains Modeling

Computing eigenvalues of semi-infinite quasi-Toeplitz matrices

An edge centrality measure based on the Kemeny constant

Palindromic linearization and numerical solution of nonsymmetric algebraic T-Riccati equations

Numerical solution of a matrix integral equation arising in Markov Modulated Lévy processes

A family of fast fixed point iterations for M/G/1-type Markov chains

Traffic lights, clumping and QBDs

A computational framework for two-dimensional random walks with restarts

Solving quadratic matrix equations arising in random walks in the quarter plane

Why is Kemeny's constant a constant?

Perron-based algorithms for the multilinear pagerank

On Functions of quasi Toeplitz matrices

On the exponential of semi-infinite quasi-Toeplitz matrices

Semi-Infinite Quasi-Toeplitz Matrices with Applications to QBD Stochastic Processes

General solution of the Poisson equation for Quasi-Birth-and-Death processes

Shift techniques for Quasi-Birth and Death processes: canonical factorizations and matrix equations

Invariant subspaces of $T$ -palindromic pencils and algebraic $T$ -Riccati equations