A Divide-and-Conquer Algorithm for the Symmetric TridiagonalEigenproblem

Authors:
Ming Gu;Stanley C. Eisenstat
Affiliations:
-;-
Venue:
SIAM Journal on Matrix Analysis and Applications
Year:
1995

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Abstract

The authors present a stable and efficient divide-and-conquer algorithm for computing the spectral decomposition of an $N \times N$ symmetric tridiagonal matrix. The key elements are a new, stable method for finding the spectral decomposition of a symmetric arrowhead matrix and a new implementation of deflation. Numerical results show that this algorithm is competitive with bisection with inverse iteration, Cuppen's divide-and-conquer algorithm, and the QR algorithm for solving the symmetric tridiagonal eigenproblem.