Memory-efficient Krylov subspace techniques for solving large-scale Lyapunov equations

Daniel Kressner
2008 2008 IEEE International Conference on Computer-Aided Control Systems  
This paper considers the solution of large-scale Lyapunov matrix equations of the form AX +XA T = −bb T . The Arnoldi method is a simple but sometimes ineffective approach to deal with such equations. One of its major drawbacks is excessive memory consumption caused by slow convergence. To overcome this disadvantage, we propose two-pass Krylov subspace methods, which only compute the solution of the compressed equation in the first pass. The second pass computes the product of the Krylov
more » ... e basis with a low-rank approximation of this solution. For symmetric A, we employ the Lanczos method; for nonsymmetric A, we extend a recently developed restarted Arnoldi method for the approximation of matrix functions. Preliminary numerical experiments reveal that the resulting algorithms require significantly less memory at the expense of extra matrix-vector products.
doi:10.1109/cacsd.2008.4627370 dblp:conf/cacsd/Kressner08 fatcat:eame625xjbetxeywn3arg2ieda