CONSTRAINED BEST APPROXIMATION IN HILBERT-SPACE Academic Article

abstract

• In this paper we study the characterization of the solution to the extremal problem inf{{norm of matrix}x{norm of matrix}x C M}, where x is in a Hilbert space H, C is a convex cone, and M is a translate of a subspace of H 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 with M is an interior point of the data cone. 1990 Springer-Verlag New York Inc.

authors

• Ward, Joseph

published proceedings

• CONSTRUCTIVE APPROXIMATION

author list (cited authors)

• CHUI, C. K., DEUTSCH, F., & WARD, J. D.

citation count

• 50

complete list of authors

• CHUI, CK||DEUTSCH, F||WARD, JD

publication date

• March 1990

publisher

• Springer Nature  Publisher

published in

• Constructive Approximation  Journal

keywords

• 49 Mathematical Sciences
• 4901 Applied Mathematics
• 4903 Numerical And Computational Mathematics

Digital Object Identifier (DOI)

• 10.1007/BF01891408

start page

• 35

end page

• 64

volume

• 6

issue

• 1

URL

• http%3A%2F%2Fdx.doi.org%2F10.1007%2Fbf01891408