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- Kantorovich_inequality abstract "In mathematics, the Kantorovich inequality is a particular case of the Cauchy-Schwarz inequality, which is itself a generalization of the triangle inequality. The triangle inequality states that the length of two sides of any triangle, added together, will be equal to or greater than the length of the third side. In simplest terms, the Kantorovich inequality translates the basic idea of the triangle inequality into the terms and notational conventions of linear programming. (See vector space, inner product, and normed vector space for 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:Let Let Then 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 Bunyakovsky inequality, the Wielandt inequality, and the Cauchy–Schwarz inequality are equivalent to the Kantorovich inequality and all of these 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.".
- Kantorovich_inequality wikiPageExternalLink index.php?page=K.html.
- Kantorovich_inequality wikiPageExternalLink Kantorovich.html.
- Kantorovich_inequality wikiPageID "929502".
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- Kantorovich_inequality hasPhotoCollection Kantorovich_inequality.
- Kantorovich_inequality title "Cauchy-Schwarz inequality".
- Kantorovich_inequality title "Kantorovich Inequality".
- Kantorovich_inequality urlname "KantorovichInequality".
- Kantorovich_inequality subject Category:Inequalities.
- Kantorovich_inequality subject Category:Mathematical_analysis.
- Kantorovich_inequality type Abstraction100002137.
- Kantorovich_inequality type Attribute100024264.
- Kantorovich_inequality type Difference104748836.
- Kantorovich_inequality type Inequalities.
- Kantorovich_inequality type Inequality104752221.
- Kantorovich_inequality type Quality104723816.
- Kantorovich_inequality comment "In mathematics, the Kantorovich inequality is a particular case of the Cauchy-Schwarz inequality, which is itself a generalization of the triangle inequality. The triangle inequality states that the length of two sides of any triangle, added together, will be equal to or greater than the length of the third side. In simplest terms, the Kantorovich inequality translates the basic idea of the triangle inequality into the terms and notational conventions of linear programming.".
- Kantorovich_inequality label "Inégalité de Kantorovitch".
- Kantorovich_inequality label "Kantorovich inequality".
- Kantorovich_inequality sameAs Inégalité_de_Kantorovitch.
- Kantorovich_inequality sameAs m.03qymw.
- Kantorovich_inequality sameAs Q3154001.
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- Kantorovich_inequality isPrimaryTopicOf Kantorovich_inequality.