MONOTONE ITERATIVE METHODS FOR NONLINEAR OPERATOR-EQUATIONS

被引：4

作者：

POTRA, FA ^{[1
]}

机构：

[1] UNIV IOWA,DEPT MATH,IOWA CITY,IA 52242

来源：

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION | 1987年 / 9卷 / 7-8期

关键词：

1. INTRODUCTION. The study of iterative procedures under partial ordering has led to monotone convergence theorems with a global character. The regions of admissible starting points provided by these theorems are considerably larger than those obtained by other means (like the local or semilocal convergence theorems in the sense of Ortega & Rheinboldt [ S ] ) . For example; let us consider the space IR endowed with the natural (componentwise) partial ordering. If the operator F : lRn --; lRn is convex and if its G-derivative F1(x) has a non- *) This work was supported in part by the National Science Foundation under Grant DMS-8503365;

D O I：

10.1080/01630568708816262

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

引用

页码：809 / 843

页数：35

共 24 条

[1]

ALEFELD G, 1980, BEITRAGE NUMERISHEN, V8, P15

[2]

BALUEV A, 1956, DOKL AKAD NAUK SSSR, V83, P781

[3]

DENNIS JE, 1974, MATH COMPUT, V28, P549, DOI 10.1090/S0025-5718-1974-0343581-1

[4] The method of successive approximations for functional equations [J].

Kantorvitch, L .

ACTA MATHEMATICA, 1939, 71 (01) :63-97

[5]

Krasnoselskii M.A., 1964, POSITIVE SOLUTION OP

[6]

MUROYA Y, 1968, MEMOIRS FS KYUSH A22, V1, P56

[7]

Ortega J.M., 1967, SIAM J NUMER ANAL, V4, P171

[8]

Ortega J.M., 1970, Iterative Solution of Nonlinear Equations in Several Variables

[9] ON THE MONOTONE CONVERGENCE OF NEWTON METHOD [J].

POTRA, FA ;

RHEINBOLDT, WC .

COMPUTING, 1986, 36 (1-2) :81-90

[10] ON A CLASS OF ITERATIVE PROCEDURES WITH MONOTONE CONVERGENCE [J].

POTRA, FA ;

SCHMIDT, JW .

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 1983, 6 (01) :1-23

← 1 2 3 →