Multiple-rank modification of symmetric eigenvalue problem.

Rank-1 modifications applied -times ( 1) often are performed to achieve a rank- modification. We propose a rank- modification for enhancing computational efficiency. As the first step toward a rank- modification, an algorithm to perform a rank-2 modification is proposed and tested. The computation cost of our proposed algorithm is in where is the cardinality of the matrix of interest. We also propose a general rank- update algorithm based on the Sturm Theorem, and compare our results to those of the direct eigenvalue decomposition and of a perturbation method.