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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(n2) arithmetic operations (ops). The same technique is used to… (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)

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

We derive a new representation of Lagrangian subspaces in the form ImΠT [ 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 |Xij | ≤ { 1 if i = j, √ 2 if i = j. This representation allows us to limit element growth in the context of doubling algorithms for the… (More)

Consider a finite set of identical computational entities that can move freely in the Euclidean 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)

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

- 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)

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 A1X + A0X + A−1 = 0 and solved by means of Cyclic Reduction (CR). It is shown that the matrices generated by CR are… (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)

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

The problem of reducing an algebraic Riccati equation XCX −AX − XD + B = 0 to a unilateral quadratic matrix equation (UQME) of the kind PX + QX + R = 0 is analyzed. New reductions are introduced which enable one to prove some theoretical and computational properties. In particular we show that the structure preserving doubling algorithm of B.D.O. Anderson… (More)