Hilbert空间中Krasnoselskii迭代算法的局部收敛性  

Local Convergence of the Krasnoselski Algorithm in Hilbert Spaces

作　　者：王朝[1] 范红磊 WANG Chao;FAN Hong-lei(School of Mathematics and Statistics,Nanjing University of Information Science and Technology,Nanjing 210044,China)

机构地区：[1]南京信息工程大学数学与统计学院,江苏南京210044

出　　处：《数学的实践与认识》2023年第2期290-296,共7页Mathematics in Practice and Theory

基　　金：国家自然科学基金面上项目(61573192)。

摘　　要：在Hilbert空间中,首先考虑了非线性算子为强半压缩和拟扩张的一个充分性条件.其次,利用Kannan不动点定理研究了Krasnoselskii迭代的局部收敛区间.最后,给出了一个数值算例来验证我们的结论.所得结果加深了对《泛函分析》课程中的Banach压缩映射原理的认识和理解.In this paper,we first consider a sufficiency condition for a mapping to be strongly demicontractive and quasi-expansive in Hilbert spaces.And then,local interval of convergence for the Krasnoselski iteration is investigated by using the Kannan fixed point theorem.Finally,a numerical example is presented to illustrate our conclusions.The results obtained deepen the understanding of the Banach contraction mapping principle in the course of functional analysis.

关 键 词：强半压缩算子 拟扩张算子 Krasnoselskii迭代 Kannan不动点定理 局部收敛区间 

分 类 号：O177.1[理学—数学]