A numerical algorithm to solve A^{T}XA - X = Q
A. Barraud · IEEE Transactions on Automatic Control · 1977
Two kinds of algorithms are usually resorted to in order to solve the well-known Lyapounov discrete equationA^{T}XA - X = Q: transformation of the original linear system in a classical one withn(n + 1)/2unknowns, and iterative scheme [1]. The first requiresn^{4}/4storage words and a cost ofn^{6}/3multiplications, which is impractical with a large system, and the second applies only ifAis a stable matrix. The solution proposed requires no stability assumption and operates in only some n2words and n3multiplications.