We study EC-$(s,t)$-weak tractability of multivariate linear problems in the average case setting. This paper extends earlier work in the worst case setting. The parameters $s\ge 0$ and $t\ge 0$ allow us to study the information complexity $n(\epsilon ,d)$ of a $d$-variate problem with respect to different powers of $ln{\epsilon }^{-1}$, corresponding to the bits of accuracy, and $d$. We consider the absolute and normalized error criteria. In particular, a multivariate problem is EC-$(s,t)$-weakly tractable iff ${lim}_{d+{\epsilon }^{-1}\to \infty }lnn(\epsilon ,d)∕[d^t+{ln}^s{\epsilon }^{-1}]=0$. We deal with general linear problems and linear tensor product problems. We show necessary and sufficient conditions for EC-$(s,t)$-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 $s>1$, in general.

我们研究EC-$（s，Ť）$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$s\ge 0$ 和 $Ť\ge 0$ 让我们研究信息的复杂性 $ñ（\epsilon ，d）$ 的 $d$关于不同权力的各种问题 $ln{\epsilon }^{-\mathrm{1个}}$，对应于精度位，以及 $d$。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-$（s，Ť）$-易处理的iff ${林}_{d+{\epsilon }^{-\mathrm{1个}}\to \infty }lnñ（\epsilon ，d）∕[d^{Ť}+{ln}^s{\epsilon }^{-\mathrm{1个}}]=0$。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$（s，Ť）$-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$s>\mathrm{1个}$， 一般来说。