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

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1989-0979938-6

Keywords:
Iterative methods,
modified Chebyshev,
moments

Article copyright:
© Copyright 1989
American Mathematical Society