INTERLACING PROPERTIES OF TRIDIAGONAL SYMMETRICAL MATRICES WITH APPLICATIONS TO PARALLEL COMPUTING

In this paper we present new interlacing properties for the eigenvalue s of an unreduced tridiagonal symmetric matrix in terms of its leading and trailing submatrices. The results stated in Hill and Parlett [SIA M J. Matrix Anal, Appl., 13 (1992), pp. 239-247] are hereby improved. We further extend our results to reduced symmetric tridiagonal matrice s and to specially structured full symmetric matrices. We then present new fast and efficient parallel algorithms for computing a few eigenv alues of symmetric tridiagonal matrices of very large order.