Heinz mean

From Wikipedia, the free encyclopedia

The Heinz mean of two non-negative real numbers A and B was defined by Bhatia[1] as:

H_x(A, B) = \frac{A^x B^{1-x} + A^{1-x} B^x}{2}.

with 0 ≤ x ≤ 1/2.

For different values of x, this Heinz mean interpolates between the arithmetic (x = 0) and geometric (x = 1/2) means such that for 0 < x < 1/2:

\sqrt{A B} = H_{1/2}(A, B) < H_x(A, B) < H_0(A, B) = \frac{A + B}{2}.

[edit] See also

[edit] References

  1. ^ R. Bathia, Interpolating the arithmetic-geometric mean inequality and its operator version, Lin. Alg. Appl., Vol. 413, p. 355-363 (2006)
This applied mathematics-related article is a stub. You can help Wikipedia by expanding it.