Result: On the solution of algebraic Riccati equations arising in fluid queues
Title:
On the solution of algebraic Riccati equations arising in fluid queues
Authors:
Source:
Special issue on the 11th ILAS conference (Coimbra, 2004)Linear algebra and its applications. 413(2-3):474-494
Publisher Information:
New York, NY: Elsevier Science, 2006.
Publication Year:
2006
Physical Description:
print, 18 ref
Original Material:
INIST-CNRS
Subject Terms:
Mathematics, Mathématiques, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Algèbre, Algebra, Algèbre linéaire et multilinéaire, matrices, Linear and multilinear algebra, matrix theory, Algèbre Cayley, Cayley algebra, Álgebra Cayley, Cyclique, Cyclic, Cíclico, Equation Riccati, Riccati equation, Ecuación Riccati, Equation algébrique, Algebraic equation, Ecuación algebraica, Equation matricielle, Matrix equation, Ecuación matricial, Equation opérateur, Operator equation, Ecuación operador, Equation quadratique, Quadratic equation, Ecuación segundo grado, Fonction logarithmique, Logarithmic function, Función logarítmica, Matrice polynomiale, Polynomial matrix, Matriz polinomial, Matrice quadratique, Quadratic matrix, Matriz cuadrática, Modèle fluide, Fluid model, Modelo fluido, Paramétrisation, Parameterization, Parametrización, Performance algorithme, Algorithm performance, Resultado algoritmo, Polynôme matriciel, Matrix polynomial, Polinomio matricial, Problème valeur propre, Eigenvalue problem, Problema valor propio, Algebraic Riccati equations, Cayley transform, Cyclic reduction, Fluid queues, Quadratic matrix equations
Document Type:
Conference
Conference Paper
File Description:
text
Language:
English
Author Affiliations:
Dipartimento di Matematica, Università di Pisa, Largo B. Pontecorvo 5, 56127 Pisa, Italy
Départment d'Informatique, U.L.B., C.P. 212, Boulevard du Triomphe, 1050 Bruxelles, Belgium
Départment d'Informatique, U.L.B., C.P. 212, Boulevard du Triomphe, 1050 Bruxelles, Belgium
ISSN:
0024-3795
Rights:
Copyright 2006 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics
Accession Number:
edscal.17520079
Database:
PASCAL Archive
Further Information
New algorithms for solving algebraic Riccati equations (ARE) which arise in fluid queues models are introduced. They are based on reducing the ARE to a unilateral quadratic matrix equation of the kind AX2 + BX + C = 0 and on applying the Cayley transform in order to arrive at a suitable spectral splitting of the associated matrix polynomial. A shifting technique for removing unwanted eigenvalues of modulus 1 is complemented with a suitable parametrization of the matrix equation in order to arrive at fast and numerically reliable solvers based on quadratically convergent iterations like logarithmic reduction and cyclic reduction. Numerical experiments confirm the very good performance of these algorithms.