### Abstract

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

Original language | English |
---|---|

Pages (from-to) | 1437-1465 |

Number of pages | 29 |

Journal | Mathematical Structures in Computer Science |

Volume | 27 |

Issue number | 8 |

DOIs | |

Publication status | Published - Dec 1 2017 |

Externally published | Yes |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Mathematics (miscellaneous)
- Computer Science Applications

### Cite this

*Mathematical Structures in Computer Science*,

*27*(8), 1437-1465. https://doi.org/10.1017/S096012951600013X

**On the computational complexity of the Dirichlet Problem for Poisson's Equation.** / Kawamura, Akitoshi; Steinberg, Florian; Ziegler, Martin.

Research output: Contribution to journal › Review article

*Mathematical Structures in Computer Science*, vol. 27, no. 8, pp. 1437-1465. https://doi.org/10.1017/S096012951600013X

}

TY - JOUR

T1 - On the computational complexity of the Dirichlet Problem for Poisson's Equation

AU - Kawamura, Akitoshi

AU - Steinberg, Florian

AU - Ziegler, Martin

PY - 2017/12/1

Y1 - 2017/12/1

N2 - 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 and thus as hard or easy as parametric Riemann integration (Friedman 1984; Ko 1991. Complexity Theory of Real Functions).

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

UR - http://www.scopus.com/inward/record.url?scp=84980410017&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84980410017&partnerID=8YFLogxK

U2 - 10.1017/S096012951600013X

DO - 10.1017/S096012951600013X

M3 - Review article

AN - SCOPUS:84980410017

VL - 27

SP - 1437

EP - 1465

JO - Mathematical Structures in Computer Science

JF - Mathematical Structures in Computer Science

SN - 0960-1295

IS - 8

ER -