Technical Report CS0832

TR#:CS0832
Class:CS
Title: A NEW DIVIDE AND CONQUER PARALLEL ALGORITHM FOR COMPUTING THE EIGENVALUES OF A SYMMETRIC TRIDIAGONAL MATRIX.
Authors: I. Bar-On
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Abstract: We present new interlacing properties for the eigenvalues of an unreduced tridiagonal symmetric matrix in terms of its leading and trailing sub matrices based on simple algebra and the Sylvester Inertia theorem. We then present a new divide and conquer parallel algorithm for computing the eigenvalues of a symmetric tridiagonal matrix. The new algorithm is more simple and straightforward than Cuppen's method [6], and does not require the computation of the corresponding eigenvectors. We can then compute the set of eigenvalues in an interval in O(kn) time, where k is the number of eigenvalues, and n is the order of the matrix.
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