A note on Q-order of convergence

被引：105

作者：

Jay, LO ^{[1
]}

机构：

[1] Univ Iowa, Dept Math, Iowa City, IA 52242 USA

来源：

BIT NUMERICAL MATHEMATICS | 2001年 / 41卷 / 02期

关键词：

convergence; metric space; Q-order; sequences;

D O I：

10.1023/A:1021902825707

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

To complement the property of Q-order of convergence we introduce the notions of Q-superorder and Q-suborder of convergence. ii new definition of exact Q-order of convergence given in this note generalizes one given by Potra. The definitions of exact Q-superorder and exact Q-suborder of convergence are also introduced. These concepts allow the characterization of any sequence converging with Q-order (at least) by showing the existence of a unique real number q is an element of [1, +infinity] such that either exact Q-order, exact Q-superorder, or exact Q-suborder q of convergence holds.

引用

页码：422 / 429

页数：8

共 10 条

[1]

[Anonymous], 1984, NONDISCRETE INDUCTIO

[2]

DENNIS JE, 1993, SIAM CLASSICS APPL M

[3]

Fletcher R., 1987, PRACTICAL METHODS OP, DOI [DOI 10.1002/9781118723203, 10.1002/9781118723203]

[4]

Gill M., 1981, Practical Optimization

[5]

Kelley C.T., 1995, ITERATIVE METHODS LI, DOI DOI 10.1137/1.9781611970944

[6]

Luenberger D.G., 1984, LINEAR NONLINEAR PRO

[7]

Nocedal J., 1999, Numerical Optimization, Vfirst, DOI DOI 10.1007/0-387-22742-3_18

[8]

Ortega JM., 1970, ITERATIVE SOLUTION N

[9] ON Q-ORDER AND R-ORDER OF CONVERGENCE [J].

POTRA, FA .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1989, 63 (03) :415-431

[10]

RHEINBOLDT W, 1998, SIAM CLASSICS APPL M

← 1 →