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- Dario Bini, Bruno Iannazzo, Federico Poloni
- SIAM J. Matrix Analysis Applications
- 2008

A special instance of the algebraic Riccati equation XCX − XE − AX + B = 0 where the n × n matrix coefficients A, B, C, E are rank structured matrices is considered. Relying on the structural properties of Cauchy-like matrices, an algorithm is designed for performing the customary Newton iteration in O(n 2) arithmetic operations (ops). The same technique is… (More)

- Federico Poloni
- 2009

We propose a new O(n)-space implementation of the GKO-Cauchy algorithm for the solution of linear systems with Cauchy-like matrix. Despite its slightly higher computational cost, this new algorithm makes a more efficient use of the processor cache memory. Thus, for matrices of size larger than n ≈ 500 − 1000, it outperforms the existing algorithms. We… (More)

- Dario Bini, Beatrice Meini, Federico Poloni
- Math. Comput.
- 2010

We propose a new matrix geometric mean satisfying the ten properties given by Ando, Li and Mathias [Linear Alg. Appl. 2004]. This mean is the limit of a sequence which converges superlinearly with convergence of order 3 whereas the mean introduced by Ando, Li and Mathias is the limit of a sequence having order of convergence 1. This makes this new mean very… (More)

- Dario Bini, Bruno Iannazzo, Beatrice Meini, Federico Poloni
- Numerical Methods for Structured Markov Chains
- 2007

We survey theoretical properties and algorithms concerning the problem of solving a nonsymmetric algebraic Riccati equation, and we report on some known methods and new algorithmic advances. In particular, some results on the number of positive solutions are proved and a careful convergence analysis of Newton's iteration is carried out in the cases of… (More)

- Volker Mehrmann, Federico Poloni
- SIAM J. Matrix Analysis Applications
- 2012

We derive a new representation of Lagrangian subspaces in the form ImΠ T I X , where Π is a symplectic matrix which is the product of a permutation matrix and a real orthogonal diagonal matrix, and X satisfies |X ij | ≤ 1 if i = j, √ 2 if i = j. This representation allows us to limit element growth in the context of doubling algorithms for the computation… (More)

We consider a special instance of the algebraic Riccati equation XCX − XE − AX + B = 0 encountered in transport theory, where the n × n matrix coefficients A, B, C, E are rank structured matrices. The equation is reduced to unilateral form A 1 X 2 + A 0 X + A −1 = 0 and solved by means of Cyclic Reduction (CR). It is shown that the matrices generated by CR… (More)

- Dario Bini, Beatrice Meini, Federico Poloni
- Numerische Mathematik
- 2010

Consider a finite set of identical entities, called robots, which can move freely in the Euclidean plane. Let p(t) denote the location of robot p at time t; a robot p can see robot q at time t if at that time no other robot lies in the line segment p(t)q(t). We consider the basic problem called Mutual Visibility: starting from arbitrary distinct locations,… (More)

- Federico Poloni, Timo Reis
- SIAM J. Matrix Analysis Applications
- 2012

We present an approach to the determination of the stabilizing solution of Lur'e matrix equations. We show that the knowledge of a certain deflating subspace of an even matrix pencil may lead to Lur'e equations which are defined on some subspace, the so-called " projected Lur'e equations. " These projected Lur'e equations are shown to be equivalent to… (More)

- Federico Poloni
- 2010

In this paper, we aim to study in an unified fashion several quadratic vector and matrix equations with nonnegativity hypotheses. Specific cases of such problems have been studied extensively in the past by several authors. For references to the single equations and results, we refer the reader to the following sections, in particular section 3. Many of the… (More)