Eigenvalue inclusion regions from inverses of shifted matrices

✍ Scribed by Michiel E. Hochstenbach; David A. Singer; Paul F. Zachlin

• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 423 KB
• Volume: 429
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/j.laa.2008.08.016

✦ Synopsis

We consider eigenvalue inclusion regions based on the field of values, pseudospectra, Gershgorin region, and Brauer region of the inverse of a shifted matrix. A family of these inclusion regions is derived by varying the shift. We study several properties, one of which is that the intersection of a family is exactly the spectrum. The numerical approximation of the inclusion sets for large matrices is also examined.