Dario Bini

activity

20062023

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

28 citations · 133 across the 22 of their papers we have counts for

collaborators

25 papers

math.NA2023

Numerical computation of the roots of Mandelbrot polynomials: an experimental analysis

Dario A. Bini

This paper deals with the problem of numerically computing the roots of polynomials $p_{k} (x)$ , $k = 1, 2, \dots$ , of degree $n = 2^{k} - 1$ recursively defined by $p_{1} (x) = x + 1$ , $p_k(x)=xp_{k…

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

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

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.NA2021★ 1 cited

Geometric means of quasi-Toeplitz matrices

Dario A. Bini, Bruno Iannazzo, Jie Meng

We study means of geometric type of quasi-Toeplitz matrices, that are semi-infinite matrices $A = (a_{i, j})_{i, j = 1, 2, \dots}$ of the form $A = T (a) + E$ , where $E$ represents a compact o…

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.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.NA2018

Quasi-Toeplitz matrix arithmetic: a MATLAB toolbox

Dario A. Bini, Stefano Massei, Leonardo Robol

A Quasi Toeplitz (QT) matrix is a semi-infinite matrix of the kind $A = T (a) + E$ where $T (a) = (a_{j - i})_{i, j \in Z^{+}}$ , $E = (e_{i, j})_{i, j \in Z^{+}}$ is compact and the norms…

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.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★ 15 cited

On the decay of the off-diagonal singular values in cyclic reduction

Dario Andrea Bini, Stefano Massei, Leonardo Robol

It was recently observed that the singular values of the off-diagonal blocks of the matrix sequences generated by the Cyclic Reduction algorithm decay exponentially. This property…

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…

math.NA2016

Efficient cyclic reduction for QBDs with rank structured blocks

Dario A. Bini, Stefano Massei, Leonardo Robol

We provide effective algorithms for solving block tridiagonal block Toeplitz systems with $m \times m$ quasiseparable blocks, as well as quadratic matrix equations with $m \times m$ …

math.NA2015★ 4 cited

Generalization of the Brauer Theorem to Matrix Polynomials and Matrix Laurent Series

Dario A. Bini, Beatrice Meini

Given a square matrix $A$ , Brauer's theorem [Duke Math. J. 19 (1952), 75--91] shows how to modify one single eigenvalue of $A$ via a rank-one perturbation, without changing any of…

math.NA2015

Computing the Exponential of Large Block-Triangular Block-Toeplitz Matrices Encountered in Fluid Queues

D. A. Bini, S. Dendievel, G. Latouche +1

The Erlangian approximation of Markovian fluid queues leads to the problem of computing the matrix exponential of a subgenerator having a block-triangular, block-Toeplitz structure…

math.NA2015★ 5 cited

Quasiseparable Hessenberg reduction of real diagonal plus low rank matrices and applications

Dario A. Bini, Leonardo Robol

We present a novel algorithm to perform the Hessenberg reduction of an $n \times n$ matrix $A$ of the form $A = D + U V^{*}$ where $D$ is diagonal with real entries and $U$ and $V$ are…

math.NA2014★ 2 cited

On a Class of Matrix Pencils and $ℓ$ -ifications Equivalent to a Given Matrix Polynomial

Dario A. Bini, Leonardo Robol

A new class of linearizations and $ℓ$ -ifications for $m \times m$ matrix polynomials $P (x)$ of degree $n$ is proposed. The $ℓ$ -ifications in this class have the form $A(x) = D…

math.NA2012★ 4 cited

Locating the eigenvalues of matrix polynomials

Dario A. Bini, Vanni Noferini, Meisam Sharify

Some known results for locating the roots of polynomials are extended to the case of matrix polynomials. In particular, a theorem by A.E. Pellet [Bulletin des Sciences Mathématique…

math.NA2012

Solving polynomial eigenvalue problems by means of the Ehrlich-Aberth method

Dario A. Bini, V. Noferini

Given the $n \times n$ matrix polynomial $P (x) = \sum_{i = 0}^{k} P_{i} x^{i}$ , we consider the associated polynomial eigenvalue problem. This problem, viewed in terms of computing the roots o…

math.NA2010★ 8 cited

On the solution of a quadratic vector equation arising in Markovian Binary Trees

Dario A. Bini, Beatrice Meini, Federico Poloni

We present some advances, both from a theoretical and from a computational point of view, on a quadratic vector equation (QVE) arising in Markovian Binary Trees. Concerning the the…