Federico Poloni
A Perron iteration for the solution of a quadratic vector equation arising in Markovian Binary Trees.
Fri, 06/04/2010 - 15:01 — SomNambulAuthors: Federico Poloni, Beatrice Meini
Subjects: Numerical Analysis
AbstractWe propose a novel numerical method for solving a quadratic vector equation
arising in Markovian Binary Trees. The numerical method consists in a fixed
point iteration, expressed by means of the Perron vectors of a sequence of
nonnegative matrices. A theoretical convergence analysis is performed. The
proposed method outperforms the existing methods for close-to-critical
problems.Quadratic Vector Equations.
Mon, 04/12/2010 - 15:01 — SomNambulAuthors: Federico Poloni
Subjects: Numerical Analysis
AbstractWe study in an unified fashion several quadratic vector and matrix equations
with nonnegativity hypotheses. Specific cases of such problems (QBD equations,
nonsymmetric algebraic Riccati equations, Lu's simple equation, Markovian
binary trees equations) have been studied extensively in the past by several
authors. Many of the results appearing here have already been proved for one or
more of the single instances of the problems, resorting to specific
characteristics of the problem.A note on the O(n)-storage implementation of the GKO algorithm.
Wed, 12/02/2009 - 16:01 — SomNambulAuthors: Federico Poloni
Subjects: Numerical Analysis
AbstractWe 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 about 500-1000,
it outperforms the existing algorithms.
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