第二类算子方程最小二乘投影法的收敛性条件（英文）

ON CONVERGENCE CONDITIONS OF LEAST-SQUARES PROJECTION METHOD FOR OPERATOR EQUATIONS OF THE SECOND KIND

本文研究针对第二类紧算子方程的最小二乘投影法的收敛条件.通过泛函分析及广义逆理论,得到了四个新的互相等价的收敛性条件,这些条件建立起了几种不同收敛性之间的联系并为人们检验逼近框架的收敛性提供了更多地选择.文中也给出了对一些简单且重要的例子的研究,以作为主要定理应用的范例.

In this paper, we investigate the convergence conditions of least-squares projection method for compact operator equations of the second kind. By technics in functional analysis and Moore-Penrose inverse, we obtain 4 new mutually equivalent convergence conditions, which build the connections among several types of convergence conditions and provide us with more choices to examine the convergency of the approximation scheme. A simple and important example is also studied as an application of the theorem.