TY - JOUR
T1 - On the computational complexity of the Dirichlet Problem for Poisson's Equation
AU - Kawamura, Akitoshi
AU - Steinberg, Florian
AU - Ziegler, Martin
N1 - Publisher Copyright:
© Cambridge University Press 2016A.
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).
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U2 - 10.1017/S096012951600013X
DO - 10.1017/S096012951600013X
M3 - Review article
AN - SCOPUS:84980410017
SN - 0960-1295
VL - 27
SP - 1437
EP - 1465
JO - Mathematical Structures in Computer Science
JF - Mathematical Structures in Computer Science
IS - 8
ER -