Faculty of Sciencehttp://hdl.handle.net/10294/1472014-04-24T22:50:46Z2014-04-24T22:50:46ZOn algebraic Riccati equations associated with M-matricesGuo, Chun-Huahttp://hdl.handle.net/10294/52582014-04-24T07:00:12Z2013-01-01T00:00:00ZOn algebraic Riccati equations associated with M-matrices
Guo, Chun-Hua
We consider the algebraic Riccati equation for which the four coefficient matrices form an $M$-matrix $K$. When $K$ is a nonsingular $M$-matrix or an irreducible singular $M$-matrix, the Riccati equation is known to have a minimal nonnegative solution
and several efficient methods are available to find this solution. In this paper we are mainly interested in the case where $K$ is a reducible singular $M$-matrix. Under a regularity assumption on the $M$-matrix $K$, we show that the Riccati equation still has a minimal nonnegative solution. We also study the properties of this particular solution and explain how the solution can be found by existing methods.
2013-01-01T00:00:00ZPerformance enhancement of doubling algorithms for a class of complex nonsymmetric algebraic Riccati equationsGuo, Chun-HuaLiu, ChangliXue, Jungonghttp://hdl.handle.net/10294/52572014-04-24T07:00:11Z2014-01-01T00:00:00ZPerformance enhancement of doubling algorithms for a class of complex nonsymmetric algebraic Riccati equations
Guo, Chun-Hua; Liu, Changli; Xue, Jungong
A new class of complex nonsymmetric algebraic Riccati equations has been studied by Liu and Xue (SIAM J. Matrix Anal. Appl., 33 (2012), 569-596), which is related to the M-matrix algebraic Riccati equations. Doubling algorithms, with properly chosen parameters, are used there for equations in this new class. It is pointed out that the number of iterations for the doubling algorithms may be relatively large in some situations. In this paper, we show that the performance of the doubling algorithms can often be improved significantly if a proper preprocessing procedure is used on the given Riccati equation. There are some difficult cases for which the preprocessing procedure does not help much by itself. We then propose new strategies for choosing parameters for doubling algorithms after using the preprocessing procedure. Numerical experiments show that our preprocessing procedure and the new parameter strategies are very effective.
2014-01-01T00:00:00ZA convergence result for matrix Riccati differential equations associated with M-matricesGuo, Chun-HuaYu, Bohttp://hdl.handle.net/10294/52562014-04-23T07:00:11Z2014-04-22T00:00:00ZA convergence result for matrix Riccati differential equations associated with M-matrices
Guo, Chun-Hua; Yu, Bo
The initial value problem for a matrix Riccati differential equation associated with an $M$-matrix is known to have a global solution $X(t)$ on $[0, \infty)$ when $X(0)$ takes values from a suitable set of nonnegative matrices. It is also known, except for the critical case, that as $t$ goes to infinity $X(t)$ converges to the minimal nonnegative solution of the corresponding algebraic Riccati equation. In this paper we present a new approach for proving the convergence, which is based on the doubling procedure and is also valid for the critical case. The approach also provides a way for solving the initial value problem and a new doubling algorithm for computing the minimal nonnegative solution of the algebraic Riccati equation.
2014-04-22T00:00:00ZIntersecting generalized permutationsBorg, PeterMeagher, Karenhttp://hdl.handle.net/10294/42912014-01-22T07:00:12Z2014-01-21T00:00:00ZIntersecting generalized permutations
Borg, Peter; Meagher, Karen
This article has been submitted to the Australiasian Journal of Combinatorics
2014-01-21T00:00:00Z