Bounds for the Entries of Matrixfunctions with Applications
نویسنده
چکیده
Let A be a symmetric matrix and let f be a smooth function deened 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.
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