Robust Satisfiability of Systems of Equations
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F15%3A00448097" target="_blank" >RIV/67985807:_____/15:00448097 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1145/2751524" target="_blank" >http://dx.doi.org/10.1145/2751524</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1145/2751524" target="_blank" >10.1145/2751524</a>
Alternative languages
Result language
angličtina
Original language name
Robust Satisfiability of Systems of Equations
Original language description
We study the problem of robust satisfiability of systems of nonlinear equations, namely, whether for a given continuous function f:K --> R^n on a finite simplicial complex K and alpha > 0, it holds that each function g:K --> R^n such that ||g-f|| <= alpha, 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 applications of topological degree and related concepts in numerical and interval analysis. Via a reverse reduction, we prove that the problem is undecidable when dim K >= 2n-2, where the threshold comes from the stable range in homotopy theory. For the lucidity of our exposition, we focus on the setting when f is simplexwise linear. Such functions can approximate general continuous functions, and thus we get approximation schemes and undecidability of the robust satisfiability in othe
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
IN - Informatics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/GBP202%2F12%2FG061" target="_blank" >GBP202/12/G061: Center of excellence - Institute for theoretical computer science (CE-ITI)</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of the ACM
ISSN
0004-5411
e-ISSN
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Volume of the periodical
62
Issue of the periodical within the volume
4
Country of publishing house
US - UNITED STATES
Number of pages
19
Pages from-to
"Article 26"
UT code for WoS article
000361200500001
EID of the result in the Scopus database
2-s2.0-84942061019