Sarah M. Moffat
Firmly nonexpansive mappings and maximally monotone operators: correspondence and duality.
Wed, 01/26/2011 - 16:01 — SomNambulAuthors: Heinz H. Bauschke, Xianfu Wang, Sarah M. Moffat
Subjects: Functional Analysis
AbstractThe notion of a firmly nonexpansive mapping is central in fixed point theory
because of attractive convergence properties for iterates and the
correspondence with maximal monotone operators due to Minty. In this paper, we
systematically analyze the relationship between properties of firmly
nonexpansive mappings and associated maximal monotone operators. Dual and
self-dual properties are also identified. The results are illustrated through
several examples.Self-dual Smooth Approximations of Convex Functions via the Proximal Average.
Wed, 03/31/2010 - 15:01 — SomNambulAuthors: Heinz H. Bauschke, Xianfu Wang, Sarah M. Moffat
Subjects: Functional Analysis
AbstractThe proximal average of two convex functions has proven to be a useful tool
in convex analysis. In this note, we express Goebel's self-dual smoothing
operator in terms of the proximal average, which allows us to give a simple
proof of self duality. We also provide a novel self-dual smoothing operator.
Both operators are illustrated by smoothing the norm.The Resolvent Average for Positive Semidefinite Matrices.
Wed, 10/21/2009 - 14:15 — SomNambulAuthors: Heinz H. Bauschke, Xianfu Wang, Sarah M. Moffat
Subjects: Functional Analysis
AbstractWe 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.The Resolvent Average for Positive Semidefinite Matrices.
Wed, 10/21/2009 - 14:15 — SomNambulAuthors: Heinz H. Bauschke, Xianfu Wang, Sarah M. Moffat
Subjects: Functional Analysis
AbstractWe 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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