一般多元线性问题的指数收敛(s,t)-弱易处理性

Exponential convergence(s,t)-weak tractability of general multivariate linear problems

在最坏框架下研究一般多元线性问题的逼近.考虑利用连续线性泛函信息类所构造的算法.对定义于Hilbert空间上的一般多元线性问题,给出了其为指数收敛(s,t)-弱易处理相匹配的充要条件,结果是基于相应的特征值序列.

The goals of this paper are to study d-variate approximation problems in the worst case setting and algorithms that use finitely many evaluations of arbitrary linear functionals. For the general multivariate linear problems defined over Hilbert spaces, we provide the matching necessary and sufficient conditions for the problems to be exponential convergence （s,t）-weakly tractable. The results are based on the corresponding non- increasing eigenvalue sequences.