侯新華 初元紅

DOI：10.7612/j.issn.10002537.2017.02.014

摘要在Hilbert空間，將外推技巧和弦線法相結(jié)合，得到新的迭代格式，用來求解奇異問題，使改進(jìn)的弦線法收斂速率由0.618 034提高到0.381 966，并通過數(shù)值例子檢驗(yàn).此結(jié)論對(duì)一般的Banach空間同樣適用.

關(guān)鍵詞Hilbert空間；弦法；奇異問題；幾何特征；收斂速率

中圖分類號(hào)O241文獻(xiàn)標(biāo)識(shí)碼A文章編號(hào)10002537（2017）02008504

The Modified Chord Method for Solving Singular Problem

HOU Xinhua1， CHU Yuanhong2*， LIU Jie2， JIANG Hongjing2

（1.Business and Tourism Department， Hunan Industry Poletechnic， Changsha 410208， China；

2.Huanghe Science and Technology College， Zhengzhou 450063， China）

AbstractIn Hilbert space， the singular problems are solved by modifying secant method and using the extrapolation technique. Our modified chord method is shown to yield a new sequence that improves the convergence rate from 0.618 034 to 0.381 966. This method is tested by numerical examples. This new approach can also be applied to a Banach space.

Key wordsHilbert space； chord method； singular problems； geometry character； convergence rate