On the computational complexity of the Dirichlet Problem for Poisson's Equation

被引：5

作者：

Kawamura, Akitoshi ^{[1
]}

Steinberg, Florian ^{[1
,2
]}

Ziegler, Martin ^{[2
]}

机构：

[1] Univ Tokyo, Grad Sch Arts & Sci, Tokyo, Japan

[2] Tech Univ Darmstadt, Dept Math, Darmstadt, Germany

来源：

MATHEMATICAL STRUCTURES IN COMPUTER SCIENCE | 2017年 / 27卷 / 08期

关键词：

REAL FUNCTIONS; COMPUTABILITY;

D O I：

10.1017/S096012951600013X

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

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 #P and thus as hard or easy as parametric Riemann integration (Friedman 1984; Ko 1991. Complexity Theory of Real Functions).

引用

页码：1437 / 1465

页数：29

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