A Stable and Efficient Algorithm for the Rank-One Modification of the Symmetric Eigenproblem

Authors:
Ming Gu;Stanley C. Eisenstat
Affiliations:
-;-
Venue:
SIAM Journal on Matrix Analysis and Applications
Year:
1994

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Abstract

An algorithm is presented for computing the eigendecomposition of a symmetric rank-one modification of a symmetric matrix whose eigendecomposition is known. Previous algorithms for this problem suffer a potential loss of orthogonality among the computed eigenvectors, unless extended precision arithmetic is used. This algorithm is based on a novel, stable method for computing the eigenvectors. It does not require extended precision and is as efficient as previous approaches.