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Inexact methods for the low rank solution to large scale Lyapunov equations
- Publication Year :
- 2018
-
Abstract
- The rational Krylov subspace method (RKSM) and the low-rank alternating directions implicit (LR-ADI) iteration are established numerical tools for computing low-rank solution factors of large-scale Lyapunov equations. In order to generate the basis vectors for the RKSM, or extend the low-rank factors within the LR-ADI method the repeated solution to a shifted linear system is necessary. For very large systems this solve is usually implemented using iterative methods, leading to inexact solves within this inner iteration. We derive theory for a relaxation strategy within these inexact solves, both for the RKSM and the LR-ADI method. Practical choices for relaxing the solution tolerance within the inner linear system are then provided. The theory is supported by several numerical examples.<br />Comment: 31 pages, 4 figures, 2 tables
- Subjects :
- Mathematics - Numerical Analysis
65F10, 65F30
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1809.06903
- Document Type :
- Working Paper