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1996•SIAM Journal on Matrix Analysis and ApplicationsRequires access

Interlacing Properties of Tridiagonal Symmetric Matrices with Applications to Parallel Computing

Ilan Bar‐On

Open publisher page 10 citations

Abstract

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

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What this paper is about

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

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Available abstract

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

Key concepts: Tridiagonal matrix, Mathematics, Eigenvalues and eigenvectors, Tridiagonal matrix algorithm, Interlacing, Symmetric matrix, Block matrix, Band matrix

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