Pronzato, Luc, Wynn, Henry P. 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
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 |
| Library of Congress subject classification: | Q Science > QA Mathematics |
| Sets: | Research centres and groups > Centre for the Analysis of Time Series (CATS) Research centres and groups > Decision Support and Risk Group (DSRG) |
| Date Deposited: | 27 Feb 2014 12:19 |
| URL: | http://eprints.lse.ac.uk/55891/ |
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