The eigenvalue shift technique and its eigenstructure analysis of a matrix

• Autores: Chun-Yueh Chiang, Matthew M. Lin
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 253, Nº 1, 2013, págs. 235-248
• Idioma: inglés
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• Resumen

  • 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.