A large literature specifies conditions under which the information complexity for a sequence of numerical problems defined for dimensions $1, 2, \ldots$ grows at a moderate rate, i.e., the sequence of problems is tractable. Here, we focus on the situation where the space of available information consists of all linear functionals and the problems are defined as linear operator mappings between Hilbert spaces. We unify the proofs of known tractability results and generalize a number of existing results. These generalizations are expressed as five theorems that provide equivalent conditions for (strong) tractability in terms of sums of functions of the singular values of the solution operators.

翻译：大量文献规定了在维度$1, 2, \ldots$上定义的数值问题序列的信息复杂度以适度速率增长的条件，即该问题序列是可处理的。本文聚焦于可用信息空间由所有线性泛函构成、且问题被定义为希尔伯特空间之间线性算子映射的情形。我们统一了已知可处理性结果的证明，并推广了若干现有结论。这些推广以五个定理的形式呈现，通过解算子奇异值函数的和给出了（强）可处理性的等价条件。