Journal of Complexity ( IF 1.8 ) Pub Date : 2019-08-13 , DOI: 10.1016/j.jco.2019.101425 Anargyros Papageorgiou , Iasonas Petras , Guiqiao Xu , Dong Yanqi
We study EC--weak tractability of multivariate linear problems in the average case setting. This paper extends earlier work in the worst case setting. The parameters and allow us to study the information complexity of a -variate problem with respect to different powers of , corresponding to the bits of accuracy, and . We consider the absolute and normalized error criteria. In particular, a multivariate problem is EC--weakly tractable iff . We deal with general linear problems and linear tensor product problems. We show necessary and sufficient conditions for EC--weak tractability. In the case of general linear problem these conditions are matching. For linear tensor product problems, we also show matching conditions with the exception of some cases where , in general.
中文翻译:
EC-平均情况下多元线性问题的-弱易处理性
我们研究EC-平均情况下的多元线性问题的-弱易处理性。本文扩展了最坏情况下的早期工作。参数 和 让我们研究信息的复杂性 的 关于不同权力的各种问题 ,对应于精度位,以及 。我们考虑绝对误差标准和标准化误差标准。特别是,多元问题是EC--易处理的iff 。我们处理一般的线性问题和线性张量积问题。我们展示了EC-的必要和充分条件-易处理性差。在一般线性问题的情况下,这些条件是匹配的。对于线性张量积问题,我们还显示了匹配条件,但在某些情况下, 一般来说。