正交投影列的强收敛准则与广义逆的Galerkin逼近  

Strong Convergence Criteria for Sequences of Orthogonal Projections and Galerkin Approximations for Generalized Inverses

作　　者：杜乃林[1] 

机构地区：[1]武汉大学数学与统计学院,武汉430072

出　　处：《数学学报（中文版）》2007年第1期43-54,共12页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(10571068)

摘　　要：对Hilbert空间上的正交投影算子列,给出其强收敛的判别准则．设{Pn}是定义在某个Hilbert空间上的一列正交投影,此准则可描述为:{Pn}是强收敛的,当且仅当{R(Pn)}满足某种适当的条件(见文中的定理2．1),这里{R(Pn)}是与{Pn}相应的值域列．作为上述准则的应用,对有界线性算子,研究其正交广义逆的Galerkin逼近方法;这一研究给出了两条一般性结果(见文中的定理3．1和定理3．2),它们可应用于第一类算子方程的近似求解问题中．Let {Pn} be a sequence of orthogonal projectia defined on a Hilbert space. One major objective of this work is to present criterions for strong convergence of {Pn}, which can be characterized as that {Pn} is strongly convergent if and only if {R （Pn）} satisfies some suitable conditions. The other objective is to present, as applications of the above criteria, some results about Galerkin projection methods for orthogonal generalized inverses, which can be applied in numerical computations of operator equation of the first kind.

关 键 词：正交投影列 广义逆 GALERKIN逼近 

分 类 号：O177.1[理学—数学] O177.92[理学—基础数学]