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

Akitoshi Kawamura, Florian Steinberg, Martin Ziegler

Research output: Contribution to journalReview article

1 Citation (Scopus)

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 languageEnglish
Pages (from-to)1437-1465
Number of pages29
JournalMathematical Structures in Computer Science
Volume27
Issue number8
DOIs
Publication statusPublished - Dec 1 2017
Externally publishedYes

Fingerprint

Complexity Theory
Complexity Classes
Poisson equation
Poisson's equation
Dirichlet Problem
Computational complexity
Computational Complexity
Theorem

All Science Journal Classification (ASJC) codes

  • Mathematics (miscellaneous)
  • Computer Science Applications

Cite this

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

In: Mathematical Structures in Computer Science, Vol. 27, No. 8, 01.12.2017, p. 1437-1465.

Research output: Contribution to journalReview article

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