Antoulas, A.C.Sorensen, D.C.Gugercin, S.2018-06-182018-06-182001-05Antoulas, A.C., Sorensen, D.C. and Gugercin, S.. "A Modified Low-Rank Smith Method for Large-Scale Lyapunov Equations." (2001) <a href="https://hdl.handle.net/1911/101972">https://hdl.handle.net/1911/101972</a>.https://hdl.handle.net/1911/101972In this note we present a modified cyclic low-rank Smith method to compute low-rank approximations to solutions of Lyapunov equations arising from large-scale dynamical systems. Unlike the original cyclic low-rank Smith method introduced by Penzl in [18], the number of the columns in the approximate solutions does not necessarily increase at each step. The number of columns required by the modified method is usually much lower than the original cyclic low-rank Smith method. The modified method never requires more columns than the original. Upper bounds are established for the errors in the low-rank approximate solutions and also for the errors in the resulting approximate Hankel singular values. Numerical results are given to verify the efficiency and accuracy of the new algorithm.19 ppengTechnical reportTR01-10