- Solves the Stein equation
S.T X S - X = -T
by mean of Smith or squared-Smith algorithm. Note that a solution X exists only if the eigenvalues of S are stricktly smaller than one, and the algorithm will not converge otherwise. The algorithm can not exploit sparsity, hence, while convergence can be improved for very large matrices, it can not be employed if matrices are too large to be stored in memory.
Ref. Penzt, “A cyclic low-rank Smith method for large sparse Lyapunov equations”, 2000.