ISSN:
1572-9265
Keywords:
41A65
;
41A29
;
41A05
;
65D05
;
Best interpolation in Hilbert space
;
implicit and explicit characterizations
;
closed linear map
;
convex constraints
;
projection
;
saddle points
;
seminorm
;
variational problem
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
,
Mathematics
Notes:
Abstract Implicit and explicit characterizations of the solutions to the following constrained best interpolation problem $$\min \left\{ {\left\| {Tx - z} \right\|:x \in C \cap A^{ - 1} d} \right\}$$ are presented. Here,T is a densely-defined, closed, linear mapping from a Hilbert spaceX to a Hilbert spaceY, A: X→Z is a continuous, linear mapping withZ a locally, convex linear topological space,C is a closed, convex set in the domain domT ofT, andd∈AC. For the case in whichC is a closed, convex cone, it is shown that the constrained best interpolation problem can generally be solved by finding the saddle points of a saddle function on the whole space, and, if the explicit characterization is applicable, then solving this problem is equivalent to solving an unconstrained minimization problem for a convex function.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02143931
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