The resolvent average for positive semidefinite matrices
Copyright policy )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.
Arithmetic mean, 47A64; 15A45; 15A24; 47H05; 90C25, Proximal average, harmonic mean, Harmonic mean, 15A45, Arithmetic average, 90C25, arithmetic mean, 15A24, Positive matrices and their generalizations; cones of matrices, Positive semi-definite matrix, Convex function, Convex functions and convex programs in convex geometry, Operator means involving linear operators, shorted linear operators, etc., resolvent average, 47A64, FOS: Mathematics, Discrete Mathematics and Combinatorics, harmonic average, convex function, Numerical Analysis, Harmonic average, Algebra and Number Theory, proximal average, 47H05, subdifferential, arithmetic average, Geometric mean, Functional Analysis (math.FA), Resolvent average, positive semidefinite matrix, Mathematics - Functional Analysis, Miscellaneous inequalities involving matrices, Fenchel conjugate, Löwner partial ordering, Geometry and Topology, Subdifferential
Arithmetic mean, 47A64; 15A45; 15A24; 47H05; 90C25, Proximal average, harmonic mean, Harmonic mean, 15A45, Arithmetic average, 90C25, arithmetic mean, 15A24, Positive matrices and their generalizations; cones of matrices, Positive semi-definite matrix, Convex function, Convex functions and convex programs in convex geometry, Operator means involving linear operators, shorted linear operators, etc., resolvent average, 47A64, FOS: Mathematics, Discrete Mathematics and Combinatorics, harmonic average, convex function, Numerical Analysis, Harmonic average, Algebra and Number Theory, proximal average, 47H05, subdifferential, arithmetic average, Geometric mean, Functional Analysis (math.FA), Resolvent average, positive semidefinite matrix, Mathematics - Functional Analysis, Miscellaneous inequalities involving matrices, Fenchel conjugate, Löwner partial ordering, Geometry and Topology, Subdifferential
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