Accession Number : ADA134542

Title :   A Characterization of an Element of Best Simultaneous Approximation.

Descriptive Note : Technical summary rept.,

Corporate Author : WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : Owens,R W

PDF Url : ADA134542

Report Date : Sep 1983

Pagination or Media Count : 15

Abstract : A basic problem of best simultaneous approximation is the following. Given a set S, two (or more) points not in S, and (possibly different) measures of the distances from the points to the set, find the element of S which is, in some sense, simultaneously closest to the given points not in S. Deutsch has suggested that some problems of best simultaneous approximation might profitably be viewed as problems of best approximation in an appropriate product space. A few authors have touched upon this approach; none, however, have pursued it consistently or developed a completed problem along such a line, even in the simplest of cases. In this paper, we show that Deutsch's suggestion can easily be carried out using known results from approximation theory to establish existence, uniqueness, and characterization results. An algorithm guaranteed to converge strongly to the element of best simultaneous approximation under certain circumstances is also proposed. (Author)

Descriptors :   *Approximation(Mathematics), Banach space, Algorithms, Set theory, Theorems

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE