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Heinz mean
In mathematics, the Heinz mean (named after E. Heinz) of two non-negative real numbers A and B, was defined by Bhatia as:
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:
The Heinz means appear naturally when symmetrizing -divergences.
It may also be defined in the same way for positive semidefinite matrices, and satisfies a similar interpolation formula.
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Heinz mean
In mathematics, the Heinz mean (named after E. Heinz) of two non-negative real numbers A and B, was defined by Bhatia as:
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:
The Heinz means appear naturally when symmetrizing -divergences.
It may also be defined in the same way for positive semidefinite matrices, and satisfies a similar interpolation formula.