Technical Report LPCR9317

TR#:LPCR9317
Class:LPCR
Title: INTERLACING PROPERTIES FOR TRIDIAGONAL SYMMETRIC MATRICES WITH APPLICATIONS TO PARALLEL COMPUTING.
Authors: I. Bar-On
PDFLPCR9317.pdf
Abstract:

We present new interlacing properties for the eigenvalues of an unreduced tridiagonal symmetric matrix in terms of its leading and trailing sub matrices. We improve upon the results stated in Hill and Parlett which are just a special case. Furthermore, our proof is elementary and simple as compared to theirs. We further generalize these results to reduced symmetric tridiagonal matrices and to specially structured full symmetric matrices. The theoretical results presented are then used for devising fast and efficient parallel algorithms for the computation of the eigenvalues of very large size matrices.

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