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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
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2008724
Page Count: 8
You can always find the topics here!Topics: Eigenvalues, Iterative methods, Polynomials, Mathematical moments, Estimation methods, Mathematics, Linear systems, Gaussian quadratures, Error rates, Matrices
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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.
Mathematics of Computation © 1989 American Mathematical Society