Kantorovich inequality [SEP] named after
are, in turn, special cases of the Hölder inequality.
The Kantorovich inequality is named after Soviet economist, mathematician, and Nobel Prize winner Leonid Kantorovich, a pioneer in the field of linear programming.
There is also Matrix version of the Kantrovich inequality due to Marshall and Olkin.
References.
- Mathematical Programming Glossary entry on "Kantorovich inequality"
- MARSHALL A. W. and OLKIN, I., Matrix versions of the Cauchy and Kantorovieh inequatities. Aequationes Mathematicae 40 (1990), pp. 89–93.
other examples of how the basic ideas inherent in the triangle inequality—line segment and distance—can be generalized into a broader context.)
More formally, the Kantorovich inequality can be expressed this way:
The Kantorovich inequality is used in convergence analysis; it bounds the convergence rate of Cauchy's steepest descent.
Equivalents of the Kantorovich inequality have arisen in a number of different fields. For instance, the Cauchy–Schwarz–Bunyakovsky inequality and the Wielandt inequality are equivalent to the Kantorovich inequality and all of these