SIAM Journal on Computing, Ahead of Print.
We show that if the nearly linear time solvers for Laplacian matrices and their generalizations can be extended to solve just slightly larger families of linear systems, then they can be used to quickly solve all systems of linear equations over the reals. This result can be viewed either positively or negatively: either nearly linear time algorithms can be developed for solving all systems of linear equations over the reals, or progress on the families that can be solved in nearly linear time will soon halt.

中文翻译：

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结构化线性系统的硬度结果

《 SIAM计算杂志》，预印本。
我们表明，如果可以扩展拉普拉斯矩阵的近似线性时间求解器及其推广来求解稍微大一些的线性系统族，那么它们可以用于快速求解所有实数线性方程组。可以正面或负面地看待这个结果：可以开发出几乎线性的时间算法来求解所有实数上的线性方程组，或者可以在几乎线性的时间内求解的族的进展将很快停止。