Efficient methods for solving a nonsymmetric algebraic Riccati equation arising in stochastic fluid models (Q2491655)

Two computational algorithms are considered for the nonsymmetric algebraic Riccati equation \(XM_{12}X+XM_{11}+M_{22}X+M_{21}=0\), where the block matrix \(M=[M_{ij}]\) is an irreducible singular \(M\)-matrix with zero row sums. The equation arises in the modelling of stochastic fluid processes. The proposed algorithms are modifications of the Schur method and the LR algorithm with a shift. Results from numerical tests are presented.