Robust Satisfiability of Systems of Equations

@article{Franek2015RobustSO,
  title={Robust Satisfiability of Systems of Equations},
  author={P. Franek and Marek Krc{\'a}l},
  journal={Journal of the ACM (JACM)},
  year={2015},
  volume={62},
  pages={1 - 19}
}
  • P. Franek, Marek Krcál
  • Published 2015
  • Mathematics, Computer Science
  • Journal of the ACM (JACM)
  • We study the problem of robust satisfiability of systems of nonlinear equations, namely, whether for a given continuous function f:K → Rn on a finite simplicial complex K and α>0, it holds that each function g:K → Rn such that ║g−f║∞ ≤ α, has a root in K. Via a reduction to the extension problem of maps into a sphere, we particularly show that this problem is decidable in polynomial time for every fixed n, assuming dim K ≤ 2n−3. This is a substantial extension of previous computational… CONTINUE READING
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