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The Resolvent Average for Positive Semidefinite Matrices
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
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