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

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 subspace 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.

Published in:
2008 Ieee International Symposium On Computer-Aided Control System Design, 207-212
Presented at:
IEEE Conference on Computer-Aided Control System Design, San Antonio, TX, Sep 03-05, 2008
Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa

 Record created 2011-05-05, last modified 2018-03-17

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