TY - JOUR
T1 - The eigenvalue shift technique and its eigenstructure analysis of a matrix
AU - Chiang, Chun Yueh
AU - Lin, Matthew M.
N1 - Funding Information:
The authors wish to thank Professor Ng and an anonymous referee for many interesting and valuable suggestions on the manuscript. This research work was partially supported by the National Science Council and the National Center for Theoretical Sciences in Taiwan .
Funding Information:
The first author was supported by the National Science Council of Taiwan under grant NSC101-2115-M-150-002 . The second author was supported by the National Science Council of Taiwan under grant NSC101-2115-M-194-007-MY3 .
PY - 2013
Y1 - 2013
N2 - The eigenvalue shift technique is the most well-known and fundamental tool for matrix computations. Applications include the search of eigeninformation, the acceleration of numerical algorithms, the study of Google's PageRank. The shift strategy arises from the concept investigated by Brauer (1952) [11] for changing the value of an eigenvalue of a matrix to the desired one, while keeping the remaining eigenvalues and the original eigenvectors unchanged. The idea of shifting distinct eigenvalues can easily be generalized by Brauer's idea. However, shifting an eigenvalue with multiple multiplicities is a challenge issue and worthy of our investigation. In this work, we propose a new way for updating an eigenvalue with multiple multiplicities and thoroughly analyze its corresponding Jordan canonical form after the update procedure.
AB - The eigenvalue shift technique is the most well-known and fundamental tool for matrix computations. Applications include the search of eigeninformation, the acceleration of numerical algorithms, the study of Google's PageRank. The shift strategy arises from the concept investigated by Brauer (1952) [11] for changing the value of an eigenvalue of a matrix to the desired one, while keeping the remaining eigenvalues and the original eigenvectors unchanged. The idea of shifting distinct eigenvalues can easily be generalized by Brauer's idea. However, shifting an eigenvalue with multiple multiplicities is a challenge issue and worthy of our investigation. In this work, we propose a new way for updating an eigenvalue with multiple multiplicities and thoroughly analyze its corresponding Jordan canonical form after the update procedure.
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U2 - 10.1016/j.cam.2013.04.024
DO - 10.1016/j.cam.2013.04.024
M3 - Article
AN - SCOPUS:84877751797
VL - 253
SP - 235
EP - 248
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
SN - 0377-0427
ER -