Suppose
are given positive numbers. Let , ..., and . Then
(1)
where
(2)
(3)
are the arithmetic and geometric mean, respectively, of the first and last numbers. The Kantorovich inequality
is central to the study of convergence properties of descent methods in optimization
(Luenberger 1984).
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the Kantorovich Inequality." Proc. Amer. Math. Soc.11, 468, 1960.
are given positive numbers. Let 
, ..., 
and 
. Then
