Federico Poloni

A Fast Newton's Method for a Nonsymmetric Algebraic Riccati Equation

A special instance of the algebraic Riccati equation

An effective matrix geometric mean satisfying the Ando-Li-Mathias properties

XCX-XE-AX+B=0

A note on the

where the

O(n)

n\times n

-storage implementation of the GKO algorithm and its adaptation to Trummer-like matrices

matrix coefficients

Quadratic vector equations

A,B,C,E

Doubling Algorithms with Permuted Lagrangian Graph Bases

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

A Perron Iteration for the Solution of a Quadratic Vector Equation Arising in Markovian Binary Trees

O(n^2)

The Pade iterations for the matrix sign function and their reciprocals are optimal

arithmetic operations (ops). The same technique is used to reduce the cost of the algorithm proposed by L.-Z. Lu in [Numer. Linear Algebra Appl., 12 (2005), pp. 191-200] from

On the solution of a quadratic vector equation arising in Markovian Binary Trees

O(n^3)