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Kantorovich-type inequalities for operators via D-optimal design theory

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

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Identification Number: 10.1016/j.laa.2005.03.022


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:
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: 16 May 2024 00:25

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