Learn More
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)
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)
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)
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)
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)
The problem of reducing an algebraic Riccati equation XCX − AX − XD + B = 0 to a unilateral quadratic matrix equation (UQME) of the kind P X 2 + 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. a suitable(More)
We propose a new O(n)-space implementation of the GKO-Cauchy algorithm for the solution of linear systems where the coefficient matrix is Cauchy-like. Moreover, this new algorithm makes a more efficient use of the processor cache memory; for matrices of size larger than n ≈ 500–1,000, it outperforms the customary GKO algorithm. We present an applicative(More)
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 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)