Krylov subspace methods for solving large Lyapunov equations

摘要: This paper considers several methods for calculating low-rank approximate solutions to large-scale Lyapunov equations of the form $AP + PA' BB' = 0$. The interest in this problem stems from model reduction where task is high-dimensional models by ones lower order. two recently developed Krylov subspace exploited are Arnoldi method [Saad, Math. Comput., 37 (1981), pp. 105–126] and Generalised Minimum Residual (GMRES) [Saad Schultz, SIAM J. Sci. Statist. 7 (1986), 856–869]. Exact expressions approximation errors incurred derived both cases. numerical solution low-dimensional linear matrix equation arising GMRES discussed an algorithm its proposed. Low rank discrete time continuous algebraic Riccati also considered. Throughout paper, authors tackle problems which B has more than one column with the...