摘要
在Hilbert空间上,讨论了在受凸集约束时,抽象线性方程的条件最小二乘解问题。得到了一般情况下解的存在性定理,研究了约束集是线性流形、一次不等式和二次不等式等特殊情形下解的存在唯一性问题,以及解集的分析表达式。
Assume that H_1, H_2 are Hilbert spaces, A∈L(H_1,H_2), h∈H_2. In this paper wediscuss the problems for the conditional least squares solution of the abstractlinear equation Ax = b with convex set constrained. The general existence theoremof solution is derived. When the constrained convex set is linear manifold orlinear inequalities or square inequalities, the existence and uniqueness conditionsof the solution are also derived. On the basis of these results, computationalmethods can be obtained.
出处
《中山大学学报（自然科学版）》
CAS
CSCD
1990年第4期7-11,共5页
Acta Scientiarum Naturalium Universitatis Sunyatseni
基金
中山大学高等学术研究中心资助项目
关键词
H空间
抽象
线性方程
最小二乘解
Hilbert space
abstract linear equation
least squares solution
convex set contrained
generalized inverse of linear operator
