Eigenvalue bounds for some classes of P-matrices

✍ Scribed by J. M. Peña

• Publisher: John Wiley and Sons
• Year: 2009
• Tongue: English
• Weight: 110 KB
• Volume: 16
• Category: Article
• ISSN: 1070-5325
• DOI: 10.1002/nla.660

✦ Synopsis

Abstract

Eigenvalue bounds are provided. It is proved that the minimal eigenvalue of a Z‐matrix strictly diagonally dominant with positive diagonals lies between the minimal and the maximal row sums. A similar upper bound does not hold for the minimal eigenvalue of a matrix strictly diagonally dominant with positive diagonals but with off‐diagonal entries with arbitrary sign. Other new bounds for nonsingular M‐matrices and totally nonnegative matrices are obtained. Copyright © 2009 John Wiley & Sons, Ltd.