摘要
本文研究了紧算子方程的Moore-Penrose广义解的逼近,引进了A-导数的概念和对应的A-光滑正则化算子.这个双参数的A-光滑正则化算子族有明显的变分意义,并且包含正则化算子作为它的特殊情形,以(修正的)截断奇异值分解方法作为它的极限情形.这些正则化算子的性质表明它们有广阔的实际应用可能性.
We study in this paper the approximation of the Moore-Penrose generalized solution to a compact operator equation and introduce A-derivatives and A-smooth regularization operators. This family of regularization operators has clear variational meanings and includes the TnXOHOB regularization method as its special case and the (modified) truncated singular value decomposition method as its limit.
出处
《高校应用数学学报（A辑）》
CSCD
北大核心
1992年第4期568-578,共11页
Applied Mathematics A Journal of Chinese Universities(Ser.A)
关键词
正则化算子
紧算子方程
M-P广义解
Ill-Posed Problems, A-Smooth Regularization Operator, Convergence Rates.
