The Resolvent Average for Positive Semidefinite Matrices

Heinz H. Bauschke, Sarah M. Moffat, Xianfu Wang

Published 2009-10-19Version 1

We define a new average - termed the resolvent average - for positive semidefinite matrices. For positive definite matrices, the resolvent average enjoys self-duality and it interpolates between the harmonic and the arithmetic averages, which it approaches when taking appropriate limits. We compare the resolvent average to the geometric mean. Some applications to matrix functions are also given.