The eigenvalue shift technique and its eigenstructure analysis of a matrix

Chun Yueh Chiang, Matthew M. Lin

Research output: Contribution to journalArticle


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.

Original languageEnglish
Pages (from-to)235-248
Number of pages14
JournalJournal of Computational and Applied Mathematics
Publication statusPublished - 2013 May 20


All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics

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