𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Optimal perturbation bounds for the Hermitian eigenvalue problem

✍ Scribed by Jesse L. Barlow; Ivan Slapničar

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
169 KB
Volume
309
Category
Article
ISSN
0024-3795

No coin nor oath required. For personal study only.

✦ Synopsis

There is now a large literature on structured perturbation bounds for eigenvalue problems of the form

where H and M are Hermitian. These results give relative error bounds on the ith eigenvalue, λ i , of the form

and bound the error in the ith eigenvector in terms of the relative gap,

In general, this theory usually restricts H to be nonsingular and M to be positive definite. We relax this restriction by allowing H to be singular. For our results on eigenvalues we

📜 SIMILAR VOLUMES

The nearest definite pair for the Hermit
The nearest definite pair for the Hermitian generalized eigenvalue problem
✍ Sheung Hun; Nicholas J. 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 199 KB

The generalized eigenvalue problem ex kfx has special properties when eY f is a Hermitian and de®nite pair. Given a general Hermitian pair eY f it is of interest to ®nd the nearest de®nite pair having a speci®ed Crawford number d b 0. We solve the problem in terms of the inner numerical radius assoc