On minimizing sequences for k-centres

J. Lember

    Research output: Contribution to journalArticleAcademicpeer-review

    6 Citations (Scopus)
    2 Downloads (Pure)

    Abstract

    Let P be a Borel measure on a separable metric space (E,d). Given an integer k1 and a nondecreasing function we seek to approximate P by a subset of E which, amongst all subsets of at most k elements, minimizes the function Wk(A,P)¿f(d(x,A))P(dx). Any set that minimizes Wk(·,P) is called a k-centre of P. We study the convergence of Wk(·,P)-minimizing sequences in noncompact spaces. As an application we prove a consistency result for empirical k-centres.
    Original languageEnglish
    Pages (from-to)20-35
    JournalJournal of Approximation Theory
    Volume120
    Issue number1
    DOIs
    Publication statusPublished - 2003

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