A Polynomial Rate of Asymptotic Regularity for Compositions of Projections in Hilbert Space

被引：8

作者：

Kohlenbach, Ulrich ^{[1
]}

机构：

[1] Tech Univ Darmstadt, Dept Math, Schlossgartenstr 7, D-64289 Darmstadt, Germany

来源：

FOUNDATIONS OF COMPUTATIONAL MATHEMATICS | 2019年 / 19卷 / 01期

关键词：

Convex feasibility problems; Asymptotic regularity; Strongly nonexpansive mappings; Proof mining; LOGICAL METATHEOREMS; BANACH; OPERATORS; BEHAVIOR; IMAGE;

D O I：

10.1007/s10208-018-9377-0

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

This paper provides an explicit polynomial rate of asymptotic regularity for (in general inconsistent) feasibility problems in Hilbert space. In particular, we give a quantitative version of Bauschke's solution of the zero displacement problem as well as of various generalizations of this problem. The results in this paper have been obtained by applying a general proof-theoretic method for the extraction of effective bounds from proofs due to the author (proof mining') to Bauschke's proof.

引用

页码：83 / 99

页数：17

共 50 条

[1] A Polynomial Rate of Asymptotic Regularity for Compositions of Projections in Hilbert Space
Ulrich Kohlenbach
[J]. Foundations of Computational Mathematics, 2019, 19 : 83 - 99
[2] Manifolds of Hilbert space projections
Levene, R. H.
Power, S. C.
[J]. PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 2010, 100 : 485 - 509
[3] NONSYMMETRIC PROJECTIONS IN HILBERT SPACE
MIZEL, VJ
RAO, MM
[J]. PACIFIC JOURNAL OF MATHEMATICS, 1962, 12 (01) : 343 - &
[4] THEOREMS ON PROJECTIONS IN HILBERT SPACE
DAVIS, C
[J]. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1954, 60 (02) : 146 - 146
[5] On pairs of projections in a hilbert space
Amrein, W.O.
Sinha, K.B.
[J]. Linear Algebra and Its Applications, 1994, 208-0
[6] ASYMPTOTIC HILBERT POLYNOMIAL AND A BOUND FOR WALDSCHMIDT CONSTANTS
Dumnicki, Marcin
Farnik, Lucja
Tutaj-Gasinska, Halszka
[J]. ELECTRONIC RESEARCH ANNOUNCEMENTS IN MATHEMATICAL SCIENCES, 2016, 23 : 8 - 18
[7] Representable Projections and Semi-Projections in a Hilbert Space
Labrousse, J-Ph
[J]. COMPLEX ANALYSIS AND OPERATOR THEORY, 2021, 15 (04)
[8] Representable Projections and Semi-Projections in a Hilbert Space
J. -Ph. Labrousse
[J]. Complex Analysis and Operator Theory, 2021, 15
[9] Inverting the difference of Hilbert space projections
Buckholtz, D
[J]. AMERICAN MATHEMATICAL MONTHLY, 1997, 104 (01): : 60 - 61
[10] A note on alternating projections in Hilbert space
Eva Kopecká
Simeon Reich
[J]. Journal of Fixed Point Theory and Applications, 2012, 12 : 41 - 47

← 1 2 3 4 5 →