Estimates of eigenvalues for iterative methods

Golub, Gene H.; Kent, Mark D.

doi:10.1090/S0025-5718-1989-0979938-6

Estimates of eigenvalues for iterative methods

Authors: Gene H. Golub and Mark D. Kent
Journal: Math. Comp. 53 (1989), 619-626
MSC: Primary 65F10; Secondary 65F15
DOI: https://doi.org/10.1090/S0025-5718-1989-0979938-6
MathSciNet review: 979938
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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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