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

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Showing 2016 · math.NAShow all

7 papers · 2 filters

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 $m \times m$ …