Generalized Mann iterates for constructing fixed points in Hilbert spaces

被引：40

作者：

Combettes, PL ^{[1
]}

Pennanen, T

机构：

[1] Univ Paris 06, Lab Jacques Louis Lions, F-75005 Paris, France

[2] Helsinki Sch Econ, Dept Management Sci, Helsinki 00101, Finland

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2002年 / 275卷 / 02期

关键词：

D O I：

10.1016/S0022-247X(02)00221-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The mean iteration scheme originally proposed by Mann is extended to a broad class of relaxed, inexact fixed point algorithms in Hilbert spaces. Weak and strong convergence results are established under general conditions on the underlying averaging process and the type of operators involved. This analysis significantly widens the range of applications of mean iteration methods. Several examples are given. (C) 2002 Elsevier Science (USA). All rights reserved.

引用

页码：521 / 536

页数：16

共 32 条

[1]

[Anonymous], 1956, INFINITE SEQUENCES S

[2] A weak-to-strong convergence principle for Fejer-monotone methods in Hilbert spaces [J].

Bauschke, HH ;

Combettes, PL .

MATHEMATICS OF OPERATIONS RESEARCH, 2001, 26 (02) :248-264

[3] Projection algorithms for solving convex feasibility problems [J].

Bauschke, HH ;

Borwein, JM .

SIAM REVIEW, 1996, 38 (03) :367-426

[4] FIXED-POINT ITERATIONS FOR REAL FUNCTIONS [J].

BORWEIN, D ;

BORWEIN, J .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1991, 157 (01) :112-126

[5]

BORWEIN J, 1992, CANAD MATH B, V35, P1

[6] CONVERGENCE THEOREMS FOR SEQUENCES OF NONLINEAR OPERATORS IN BANACH SPACES [J].

BROWDER, FE .

MATHEMATISCHE ZEITSCHRIFT, 1967, 100 (03) :201-&

[7] An example on the Mann iteration method for Lipschitz pseudocontractions [J].

Chidume, CE ;

Mutangadura, SA .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2001, 129 (08) :2359-2363

[8]

Combettes, 2001, INHERENTLY PARALLEL, V8, P115, DOI DOI 10.1016/S1570-579X(01)80010-0

[9] Convex set theoretic image recovery by extrapolated iterations of parallel subgradient projections [J].

Combettes, PL .

IEEE TRANSACTIONS ON IMAGE PROCESSING, 1997, 6 (04) :493-506

[10]

COMBETTES PL, 1995, CR ACAD SCI I-MATH, V320, P1385

← 1 2 3 4 →