Kantorovich-type inequalities for operators via D-optimal design theory
Pronzato, L., Wynn, H. P.
& Zhigljavsky, A. A.
(2005).
Kantorovich-type inequalities for operators via D-optimal design theory.
Linear Algebra and Its Applications,
410, 160-169.
https://doi.org/10.1016/j.laa.2005.03.022
& Zhigljavsky, A. A.
(2005).
Kantorovich-type inequalities for operators via D-optimal design theory.
Linear Algebra and Its Applications,
410, 160-169.
https://doi.org/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.