A stability-enhancing scaling procedure for Schur-Riccati solvers
Systems & Control Letters
On the Solution of a Nonlinear Matrix Equation arising in Queueing Problems
SIAM Journal on Matrix Analysis and Applications
A new method for computing the stable invariant subspace of a real Hamiltonian matrix
Journal of Computational and Applied Mathematics - Special issue: dedicated to William B. Gragg on the occasion of his 60th Birthday
Analysis and modification of Newton's method for algebraic Riccati equations
Mathematics of Computation
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
SIAM Journal on Matrix Analysis and Applications
A Shifted Cyclic Reduction Algorithm for Quasi-Birth-Death Problems
SIAM Journal on Matrix Analysis and Applications
Nonsymmetric Algebraic Riccati Equations and Wiener--Hopf Factorization for M-Matrices
SIAM Journal on Matrix Analysis and Applications
On the Iterative Solution of a Class of Nonsymmetric Algebraic Riccati Equations
SIAM Journal on Matrix Analysis and Applications
Comments on a Shifted Cyclic Reduction Algorithm for Quasi-Birth-Death Problems
SIAM Journal on Matrix Analysis and Applications
Computers & Mathematics with Applications
Convergence analysis of a variant of the Newton method for solving nonlinear equations
Computers & Mathematics with Applications
The eigenvalue shift technique and its eigenstructure analysis of a matrix
Journal of Computational and Applied Mathematics
Monotone convergence of Newton-like methods for M-matrix algebraic Riccati equations
Numerical Algorithms
Hi-index | 7.29 |
We consider the nonsymmetric algebraic Riccati equation XM12X+XM11+M22X+M21=0, where M11, M12, M21, M22 are real matrices of sizes n × n, n × m, m × n, m × m, respectively, and M = [Mij]2i,j=1 is an irreducible singular M-matrix with zero row sums. The equation plays an important role in the study of stochastic fluid models, where the matrix-M is the generator of a Markov chain. The solution of practical interest is the minimal nonnegative solution. This solution may be found by basic fixed-point iterations, Newton's method and the Schur method. However, these methods run into difficulties in certain situations. In this paper we provide two efficient methods that are able to find the solution with high accuracy even for these difficult situations.