Existence of a low rank or ℋ-matrix approximant to the solution of a Sylvester equation

Numerical Linear Algebra with Applications

Volumn 11, Issue 4, 2004, Pages 371-389

  Grasedyck, L ^a  

^a MAX PLANCK INSTITUTE FOR MATHEMATICS IN THE SCIENCES   (Germany)

Author keywords

Data sparse approximation; Hierarchical matrices; Low rank approximation; Singular value bounds; Sylvester equation

Indexed keywords

EID: 10044281868     PISSN: 10705325     EISSN: None     Source Type: Journal    
DOI: 10.1002/nla.366     Document Type: Article

References (4)

1. Lancaster P. Explicit solutions of linear matrix equations. SIAM Review 1970; 12:544-566.
2. Hackbusch W. A sparse matrix arithmetic based on ℋ-matrices. Part I: Introduction to ℋ-matrices. Computing 2000; 62:89-108.
3. Penzl T. Eigenvalue decay bounds for solutions of Lyapunov equations: the symmetric case. Systems and Control Letters 2000; 40(2):139-144.
4. Sorensen D, Zhou Y. Bounds on eigenvalue decay rates and sensitivity of solutions to Lyapunov equations. Preprint Rice University Houston, Texas 2002; http://www.caam.rice.edu/caam/trs/tr02.html#TR02-07 [25 June 2002].