On the computational complexity of the Dirichlet Problem for Poisson's Equation
On the computational complexity of the Dirichlet Problem for Poisson's Equation
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DOI：
10.1017/s096012951600013x
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发表时间：
2016-07
影响因子：
0.5
通讯作者：
A. Kawamura;Florian Steinberg;M. Ziegler
中科院分区：
文献类型：
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作者：
A. Kawamura;Florian Steinberg;M. Ziegler
在过去的几年里，人们越来越有兴趣根据经典数学定理的强度对其进行分类（存在性声明）。我们从计算复杂性的精确角度来追求这一目标。具体地说，我们建立严格解决泊松方程的狄利克雷问题是在一个精确的意义上的“完整”的复杂性类${\#\mathcal{P}}$，因此作为硬或容易参数黎曼积分（弗里德曼1984年;高1991年。真实的函数的复杂性理论）。
The last years have seen an increasing interest in classifying (existence claims in) classical mathematical theorems according to their strength. We pursue this goal from the refined perspective of computational complexity. Specifically, we establish that rigorously solving the Dirichlet Problem for Poisson's Equation is in a precise sense ‘complete’ for the complexity class ${\#\mathcal{P}}$ and thus as hard or easy as parametric Riemann integration (Friedman 1984; Ko 1991. Complexity Theory of Real Functions).