  Rank-1 modifications in k-times (k > 1) often are performed to achieve rank-k
modification. We propose a rank- k modification for enhancing computational
efficiency. As the first step towards a rank- k modification, an algorithm to
perform rank-2 modification is proposed and tested. The computation cost of our
proposed algorithm is in O(n^1.5). We also propose a general rank- k update
algorithm based upon the modified Sturm Theorem, and compare our results from
those of the direct eigenvalue decomposition and of a perturbation method.
