Quadratic convergence of Newton's method for convex interpolation and smoothing

被引：24

作者：

Dontchev, AL ^{[1
]}

Qi, HD

Qi, LQ

机构：

[1] Math Reviews, Ann Arbor, MI 48107 USA

[2] Univ New S Wales, Sch Math, Sydney, NSW 2052, Australia

[3] Hong Kong Polytech Univ, Dept Math Appl, Kowloon, Hong Kong, Peoples R China

来源：

CONSTRUCTIVE APPROXIMATION | 2003年 / 19卷 / 01期

关键词：

D O I：

10.1007/s00365-002-0513-2

中图分类号：

O1 [数学];

学科分类号：

0701 [数学]; 070101 [基础数学];

摘要：

In this paper, we prove that Newton's method for convex best interpolation is locally quadratically convergent, giving an answer to a question of Irvine, Marin, and Smith [7] and strengthening a result of Andersson and Elfving [1] and our previous work [5]. A damped New,ton-type method is presented which has global quadratic convergence. Analogous results are obtained for the convex smoothing problem. Numerical examples are presented.

引用

页码：123 / 143

页数：21

共 15 条

[1]

AN ALGORITHM FOR CONSTRAINED INTERPOLATION [J].