On the optimality and sharpness of Laguerre's lower bound on the smallest eigenvalue of a symmetric positive definite matrix

• Published in: arXiv.org
• Main Author: Yamamoto, Yusaku
• Format: Paper
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 01.02.2017
• Subjects: Algorithms; Eigenvalues; Iterative methods; Lower bounds; Mathematical analysis; Matrix methods; Optimization; Sharpness

Lower bounds on the smallest eigenvalue of a symmetric positive definite matrices \(A\in\mathbb{R}^{m\times m}\) play an important role in condition number estimation and in iterative methods for singular value computation. In particular, the bounds based on \({\rm Tr}(A^{-1})\) and \({\rm Tr}(A^{-2...