A survey of some estimates of eigenvalues and condition numbers for certain preconditioned matrices

Axelsson, Owe and Lu, Hao (1997) A survey of some estimates of eigenvalues and condition numbers for certain preconditioned matrices. Journal of Computational and Applied Mathematics, 80 (2). pp. 241-264. ISSN 0377-0427

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Abstract:	Eigenvalue and condition number estimates for preconditioned iteration matrices provide the information required to estimate the rate of convergence of iterative methods, such as preconditioned conjugate gradient methods. In recent years various estimates have been derived for (perturbed) modified (block) incomplete factorizations. We survey and extend some of these and derive new estimates. In particular we derive upper and lower estimates of individual eigenvalues and of condition number. This includes a discussion that the condition number of preconditioned second order elliptic difference matrices is O(h-1). Some of the methods are applied to compute certain parameters involved in the computation of the preconditioner.
Item Type:	Article
Copyright:	© 1997 Elsevier
Faculty:	Electrical Engineering, Mathematics and Computer Science (EEMCS)
Research Group:	Mathematics of Computational Science (MaCS)
Link to this item:	http://purl.utwente.nl/publications/73763
Official URL:	http://dx.doi.org/10.1016/S0377-0427(97)00023-X
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