Title of article :
A survey of some estimates of eigenvalues and condition numbers for certain preconditioned matrices
Author/Authors :
Axelsson، نويسنده , , Owe and Lu، نويسنده , , Hao، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 1997
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.
Keywords :
Preconditioning method , Eigenvalue bound , Condition number estimate , Perturbation
Journal title :
Journal of Computational and Applied Mathematics
Journal title :
Journal of Computational and Applied Mathematics