Читать книгу The Big R-Book - Philippe J. S. De Brouwer - Страница 270

One particular generalized mean is the power mean or Hölder mean. It is defined for a set of K positive numbers x_k by

holder mean

mean – holder

by choosing particular values for m one can get the quadratic, arithmetic, geometric and harmonic means.

mean – quadratic

m → ∞: maximum of x_k

m = 2: quadratic mean

m = 1: arithmetic mean

m → 0: geometric mean

m = 1: harmonic mean

m → −∞: minimum of x_k