假設 
是給定的 正 數。令 
, ..., 
和 
。則
 |
(1)
|
其中
 |  |  |
(2)
|
 |  |  |
(3)
|
分別是第一個和最後一個數的算術平均值和幾何平均值。Kantorovich 不等式對於研究最佳化中下降方法的收斂性至關重要 (Luenberger 1984)。
Kantorovich 不等式
另請參閱
算術平均值, 幾何平均值使用 探索
參考文獻
Bauer, F. L. "A Further Generalization of the Kantorovich Inequality." Numer. Math. 3, 117-119, 1961.Greub, W. and Rheinboldt, W. "On a Generalization of an Inequality of L. V. Kantorovich." Proc. Amer. Math. Soc. 10, 407-413, 1959.Henrici, P. "Two Remarks of the Kantorovich Inequality." Amer. Math. Monthly 68, 904-906, 1961.Kantorovič, L. V. "Functional Analysis and Applied Mathematics" [Russian]. Uspekhi Mat. Nauk 3, 89-185, 1948.Luenberger, D. G. Linear and Nonlinear Programming, 2nd ed. Reading, MA: Addison-Wesley, pp. 217-219, 1984.Newman, M. "Kantorovich's Inequality." J. Res. National Bur. Standards 64B, 33-34, 1960.Pólya, G. and Szegö, G. Aufgaben und Lehrsätze der Analysis. Berlin: Springer-Verlag, 1925.Pták, V. "The Kantorovich Inequality." Amer. Math. Monthly 102, 820-821, 1995.Schopf, A. H. "On the Kantorovich Inequality." Numer. Math. 2, 344-346, 1960.Strang, W. G. "On the Kantorovich Inequality." Proc. Amer. Math. Soc. 11, 468, 1960.在 中被引用
Kantorovich 不等式請引用為
Weisstein, Eric W. "Kantorovich 不等式。" 來自 Web 資源。 https://mathworld.tw/KantorovichInequality.html