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 $AX^2+BX+C=0$ 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.
On the solution of Riccati equations arising in fluid queues
IANNAZZO, Bruno;
2006
Abstract
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 $AX^2+BX+C=0$ 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
