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Estimates of Eigenvalues for Iterative Methods

Gene H. Golub and Mark D. Kent
Mathematics of Computation
Vol. 53, No. 188 (Oct., 1989), pp. 619-626
DOI: 10.2307/2008724
Stable URL: http://www.jstor.org/stable/2008724
Page Count: 8
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Estimates of Eigenvalues for Iterative Methods
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Abstract

We describe a procedure for determining estimates of the eigenvalues of operators used in various iterative methods for the solution of linear systems of equations. We also show how to determine upper and lower bounds for the error in the approximate solution of linear equations, using essentially the same information as that needed for the eigenvalue calculations. The methods described depend strongly upon the theory of moments and Gauss quadrature.

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