用修正的割线法求解奇异问题  

The Modified Secant Method for Solving Singular Problem

作　　者：初元红[1] 马红娟[1] 郑喜英[1] 

机构地区：[1]黄河科技学院,中国郑州450063

出　　处：《湖南师范大学自然科学学报》2017年第6期87-92,共6页Journal of Natural Science of Hunan Normal University

基　　金：河南省教育厅资助项目(14B110024);郑州市科技局资助项目(20141374;20141375);黄河科技学院教改资助项目(JM2012014)

摘　　要：为了求解奇异问题,在Hilbert空间中,将割线法和外推技巧相结合得到新的迭代格式,其收敛速率为0.3.未改进的割线法的收敛速率0.618,改进的割线法收敛速率得到大大的提高.同时,该算法对于一般的Banach空间同样适用.最后,通过数值实验验证了这一结果.In Hilbert space, we modified secant method with the extrapolation technique in order to solve the singular problems. The convergence rate of the new iteration is 0.3 rather than 0. 618 of the original. So the convergence rate of the modified secant method is distinctively improved, which is also applicable to the general Banach space. Finally, numerical experiment is presented to confirm this result.

关 键 词：HILBERT空间 改进的割线法 奇异问题 几何特征 收敛速率 

分 类 号：O241[理学—计算数学]