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On the eigenvalue distribution of a class of preconditioning methods (1986)

Axelsson, Owe ; Lindskog, Gunhild

Springer

Numerische Mathematik 48 (1986), S. 479-498

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ISSN: 0945-3245

Keywords: AMS(MOS): 65F10 ; CR: G1. 3

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Summary A class of preconditioning methods depending on a relaxation parameter is presented for the solution of large linear systems of equationAx=b, whereA is a symmetric positive definite matrix. The methods are based on an incomplete factorization of the matrixA and include both pointwise and blockwise factorization. We study the dependence of the rate of convergence of the preconditioned conjugate gradient method on the distribution of eigenvalues ofC −1 A, whereC is the preconditioning matrix. We also show graphic representations of the eigenvalues and present numerical tests of the methods.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01389447

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