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In this paper, we present a generalized Cuppen's divide-and-conquer algorithmfor the symmetric tridiagonal eigenproblem. We extend the Cuppen's work to therank two modifications of the form $A =T +\beta_1\bw_1\bw_1^T +\beta_2\bw_2\bw_2^T$, where $T$ is a block tridiagonal matrix having threeblocks. We introduce a new deflation technique and obtain a secular equation,for which the distribution of eigenvalues is nontrivial. We present a way tocount the number of eigenvalues in each subinterval. It turns out that eachsubinterval contains either none, one or two eigenvalues. Furthermore,computing eigenvectors preserving the orthogonality are also suggested. Somenumerical results, showing our algorithm can calculate the eigenvalue twice asfast as the Cuppen's divide-and-conquer algorithm, are included.

A generalization of the divide and conquer algorithm for the symmetric tridiagonal eigenproblem