, Volume 12, Issue 4, pp 543-554

The method of conjugate gradients used in inverse iteration

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Abstract

An algorithm is devised that improves an eigenvector approximation corresponding to the largest (or smallest) eigenvalue of a large and sparse symmetric matrix. It solves the linear systems that arise in inverse iteration by means of the c-g algorithm. Stopping criteria are developed which ensure an accurate result, and in many cases give convergence after a small numer of c-g steps.