Abstract
The conjugate gradient method for the iterative solution of a set of linear equationsAx=b is essentially equivalent to the Lanczos method, which implies that approximations to certain eigen-values ofA can be obtained at low cost. In this paper it is shown how the smallest “active” eigenvalue ofA can be cheaply approximated, and the usefulness of this approximation for a practical termination criterion for the conjugate gradient method is studied. It is proved that this termination criterion is reliable in many relevant situations.
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