ISSN:
1572-9125
Keywords:
Matrix functions
;
quadrature rules
;
Lanczos process
;
band matrices
;
exponential decay
;
preconditioned conjugate gradients
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Let A be a symmetric matrix and let f be a smooth function defined on an interval containing the spectrum of A. Generalizing a well-known result of Demko, Moss and Smith on the decay of the inverse we show that when A is banded, the entries of f(A)are bounded in an exponentially decaying manner away from the main diagonal. Bounds obtained by representing the entries of f(A)in terms of Riemann-Stieltjes integrals and by approximating such integrals by Gaussian quadrature rules are also considered. Applications of these bounds to preconditioning are suggested and illustrated by a few numerical examples.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1022362401426
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