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- Tayyebe Haqiri, Federico Poloni
- J. Computational Applied Mathematics
- 2017

Consider a finite set of identical computational entities that can move freely in the Eu-clidean plane operating in Look-Compute-Move cycles. Let p(t) denote the location of entity p at time t; entity p can see entity q at time t if at that time no other entity lies on the line segment p(t)q(t). We consider the basic problem called Mutual Visibility:… (More)

- Volker Mehrmann, Federico Poloni
- Numerical Lin. Alg. with Applic.
- 2016

The numerical computation of Lagrangian invariant subspaces of large scale Hamiltonian matrices is discussed in the context of the solution of Lyapunov and Riccati equations. A new version of the low-rank alternating direction implicit method is introduced, which in order to avoid numerical difficulties with solutions that are of very large norm, uses an… (More)

- Federico Poloni, Timo Reis
- Numerical Lin. Alg. with Applic.
- 2016

Markov-modulated Brownian motion is a popular tool to model continuous-time phenomena in a stochastic context. The main quantity of interest is the invariant density, which satisfies a differential equation associated with the quadratic matrix polynomial P (z) = V z−Dz+Q, where the matrices V and D are diagonal and Q is the transition matrix of a… (More)

- Federico Poloni, Nataša Strabi, Nataša Strabić
- 2015

Lagrangian subspaces are linear subspaces that appear naturally in control theory applications, and especially in the context of algebraic Riccati equations. We introduce a class of semidefinite Lagrangian subspaces and show that these subspaces can be represented by a subset I ⊆ {1, 2, . . . , n} and a Hermitian matrix X ∈ Cn×n with the property that the… (More)

We describe a procedure based on the Krawczyk method to compute a verified enclosure for the stabilizing solution of a continuoustime algebraic Riccati equation A∗X + XA + Q = XGX, building on the work of [B. Hashemi, SCAN 2012] and adding several modifications to the Krawczyk procedure. Moreover, we describe a new O(n) direct method for verification, based… (More)

The Hodrick-Prescott filter represents one of the most popular method for trendcycle extraction in macroeconomic time series. In this paper we provide a multivariate generalization of the Hodrick-Prescott filter, based on the seemingly unrelated time series approach. We first derive closed-form expressions linking the signal-noise matrix ratio to the… (More)

- Giang T. Nguyen, Federico Poloni
- Numerische Mathematik
- 2015

Markov-modulated fluid queues are popular stochastic processes frequently used for modelling real-life applications. An important performance measure to evaluate in these applications is their steady-state behaviour, which is determined by the stationary density. Computing it requires solving a (nonsymmetric) M-matrix algebraic Riccati equation, and indeed… (More)

The delay Lyapunov equation is an important matrix boundary-value problem which arises as an analogue of the Lyapunov equation in the study of time-delay systems ẋ(t) = A0x(t) +A1x(t− τ) +B0u(t). We propose a new algorithm for the solution of the delay Lyapunov equation. Our method is based on the fact that the delay Lyapunov equation can be expressed as a… (More)