Concept

Generalized mean

Summary
In mathematics, generalized means (or power mean or Hölder mean from Otto Hölder) are a family of functions for aggregating sets of numbers. These include as special cases the Pythagorean means (arithmetic, geometric, and harmonic means). Definition If p is a non-zero real number, and x_1, \dots, x_n are positive real numbers, then the generalized mean or power mean with exponent p of these positive real numbers is M_p(x_1,\dots,x_n) = \left( \frac{1}{n} \sum_{i=1}^n x_i^p \right)^{{1}/{p}} . (See p-norm). For p = 0 we set it equal to the geometric mean (which is the limit of means with exponents approaching zero, as proved below): M_0(x_1, \dots, x_n) = \left(\prod_{i=1}^n x_i\right)^{1/n} . Furthermore, for a sequence of positive weights wi we define the weighted power mean as
About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.
Related publications

Loading

Related people

Loading

Related units

Loading

Related concepts

Loading

Related courses

Loading

Related lectures

Loading