Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9498163 | Linear Algebra and its Applications | 2005 | 10 Pages |
Abstract
The Kantorovich inequality is zTAzzTAâ1z ⩽ (M + m)2/(4mM), where A is a positive definite symmetric operator in Rd, 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 Rd 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.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Luc Pronzato, Henry P. Wynn, Anatoly Zhigljavsky,