ISSN:
1432-0940
Keywords:
Conical hull
;
Polar of a cone
;
Best constrained interpolation
;
Primary 41A65
;
Secondary 41A29
;
41A05
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract In this paper we study the characterization of the solution to the extremal problem inf{‖x‖x ∈C ∩M}, wherex is in a Hilbert spaceH, C is a convex cone, andM is a translate of a subspace ofH determined by interpolation conditions. We introduce a simple geometric property called the “conical hull intersection property” that provides a unifying framework for most of the basic results in the subject of optimal constrained approximation. Our approach naturally lends itself to considering the data cone as opposed to the constraint cone. A nice characterization of the solution occurs, for example, if the data vector associated withM is an interior point of the data cone.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01891408
