Explore relationships

Smooth maximum

In mathematics, a smooth maximum of an indexed familyx1, ..., xn of numbers is a smooth approximation to the maximum function max(x1,…,xn),{\displaystyle \max(x_{1},\ldots ,x_{n}),} meaning a parametric family of functions mα(x1,…,xn){\displaystyle m_{\alpha }(x_{1},\ldots ,x_{n})} such that for every ⁠α{\displaystyle \alpha }⁠, the function ⁠mα{\displaystyle m_{\alpha }}⁠ is smooth, and the family converges to the maximum function ⁠mα→max{\displaystyle m_{\alpha }\to \max }⁠ as ⁠α→∞{\displaystyle \alpha \to \infty }⁠.

Use + to expand a branch. Click a topic name to open its summary.