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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 . Although these iterations, with customary initialization, converge sublinearly whe…
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…
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…
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…
On certain matrix algebras related to quasi-Toeplitz matrices
Dario Bini, Beatrice Meini
Let be the semi-infinite tridiagonal matrix having subdiagonal and superdiagonal unit entries, , where , and zero elsewhere. A basis $\{P_0,P_1,P…
On Kemeny's constant and stochastic complement
Dario Andrea Bini, Fabio Durastante, Sooyeong Kim +1
Given a stochastic matrix partitioned in four blocks , , Kemeny's constant is expressed in terms of Kemeny's constants of the stochastic complements $P_…