Pronzato, Luc, Wynn, Henry P. 
ORCID: 0000-0002-6448-1080 and Zhigljavsky, Anatoly A
(2005)
Kantorovich-type inequalities for operators via D-optimal design theory.
Linear Algebra and Its Applications, 410.
pp. 160-169.
ISSN 0024-3795
Identification Number: 10.1016/j.laa.2005.03.022
Abstract
The Kantorovich inequality is zTAzzTA−1z ⩽ (M + m)2/(4mM), where A is a positive definite symmetric operator in RdRd, z is a unit vector and m and M are respectively the smallest and largest eigenvalues of A. This is generalised both for operators in RdRd and in Hilbert space by noting a connection with D-optimal design theory in mathematical statistics. Each generalised bound is found as the maxima of the determinant of a suitable moment matrix.
| Item Type: | Article |
|---|---|
| Official URL: | http://www.journals.elsevier.com/linear-algebra-an... |
| Additional Information: | © 2005 The Author |
| Divisions: | Centre for Analysis of Time Series |
| Subjects: | Q Science > QA Mathematics |
| Date Deposited: | 27 Feb 2014 12:19 |
| Last Modified: | 04 Jan 2024 06:27 |
| URI: | http://eprints.lse.ac.uk/id/eprint/55891 |
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