Structured perturbation analysis for an infinite size quasi-Toeplitz matrix equation with applications (Q2045168)

Linear matrix equations involving semi-infinite matrices which have a quasi-Toeplitz structure arise in different settings, mostly connected with partial differential equations or with the study of Markov chains, such as random walks on bidimensional lattices. The authors study one of such equations that generalises the Sylvester equation \(AX + X B = C\), quite popular in control theory. This equation reads \(AX B + C X D = E\), where \(A, B, C, D, E\) are infinite size matrices with a quasi Toeplitz structure, that is, a semi-infinite Toeplitz matrix plus an infinite size compact correction matrix.