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The Angle Between Subspaces of a Hilbert Space
This is a mainly expository paper concerning two different definitions of the angle between a pair of subspaces of a Hilbert space, certain basic results which hold for these angles, and a few of the
A Dual Approach to Constrained Interpolationfrom a Convex Subset of Hilbert Space
Many interesting and important problems of best approximationare included in (or can be reduced to) one of the followingtype: in a Hilbert spaceX, find the best approximationPK(x) to anyx?Xfrom the
Continuous Selections and Approximate Selection for Set-Valued Mappings and Applications to Metric Projections
Two new continuity properties for set-valued mappings are defined which are weaker than lower semicontinuity. One of these properties characterizes when approximate selections exist. A few selection
Minimizing certain convex functions over the intersection of the fixed point sets of nonexpansive mappings
Let T i (i = 1,2,...,N) be nonexpansive mappings on a Hilbert space H, and let ⊖: H → R∪{∞} be a function which has a uniformly strongly positive and uniformly bounded second (Frechet) derivative
Best approximation in inner product spaces
Inner Product Spaces.- Best Approximation.- Existence and Uniqueness of Best Approximations.- Characterization of Best Approximations.- The Metric Projection.- Bounded Linear Functionals and Best
The Method of Alternating Orthogonal Projections
The method of alternating orthogonal projections is discussed, and some of its many and diverse applications are described.
The rate of convergence of dykstra's cyclic projections algorithm: The polyhedral case
Suppose K is the intersection of a finite number of closed half-spaces in a Hilbert space X. Starting with any point xeX, it is shown that the sequence of iterates {x n } generated by Dykstra's
Accelerating the convergence of the method of alternating projections
The powerful von Neumann-Halperin method of alternating projections (MAP) is an algorithm for determining the best approximation to any given point in a Hilbert space from the intersection of a
The Rate of Convergence for the Method of Alternating Projections, II
Abstract The purpose of the paper is threefold: (1) To develop a useful error bound for the method of alternating projections which is relatively easy to compute and remember; (2) To exhibit a
Constrained best approximation in Hilbert space
TLDR
A simple geometric property called the “conical hull intersection property” is introduced that provides a unifying framework for most of the basic results in the subject of optimal constrained approximation.
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