Continuous Selections for Metric Projections and Interpolating SubspacesThe existence of continuous selections for metric projections is the theoretical foundation of the existence of stable algorithms for computing best approximation elements. In this monograph we will give various intrinsic characterizations of subspaces of C o(T) which ensure the existence of continuous metric selections. Since the Chebyshev approximation is a special case of semi-infinite optimization, we hope that our study will give some insight to stability problems in semi-infinite optimization as well as parametric optimizations. |
Contents
Introduction | 1 |
Extremal Signatures | 9 |
Invariance of Regular Weakly Interpolating Subspaces | 19 |
Copyright | |
10 other sections not shown
Common terms and phrases
a₁ alternation element alternation signature Approx approximation of ƒ approximation theory B₁ bdZ(g C Z(g card(A card(bdZ(g card(supp card(Z(g change signs Chebyshev alternation phenomena continuous function continuous metric selections continuous selection contradicts Corollary 4.2 Define Definition 7.2 deg(g Deutsch dim G dim G(int Z(g dim G(T dim G|{y dim G|A element of ƒ exist neighborhoods existence of continuous finite finite-dimensional subspace ƒ from G g E G G satisfies NS(0 G(supp G₁ int{x intZ(g intZ(G(A Lemma Let g Lipschitz continuous lower semicontinuity Math metric projections nonempty Nürnberger and Sommer PG(f primitive extremal signature proved quasi-Haar subspace regular weakly interpolating selections for metric sign changes signature of G span{g spline functions strict best approximation Strong unicity subset supp Suppose that G Theorem 4.2 V₁ W₁ weak Chebyshev subspace weakly interpolating subspace X₁ Z-subspace zero interval zeros with sign σα