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A new iterative method of finding the minimum eigenvalue of a symmetric matrix is described. This method does not utilize matrix inversions and is applicable to any matrix R for which the matrix-vector product Rx is rapidly computable. It seeks the minimum eigenvalue of R by minimizing the quadratic form X T Rx on the unit hypersphere, using a search technique derived from the conjugate gradient method. The computational complexity of each step of the algorithm depends on the speed with which Rx can be computed.
Fuhrmann et al. (Thu,) studied this question.