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_____%2F14%3A00427751" target="_blank" >RIV/67985807:_____/14:00427751 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1137/1.9781611973402.14" target="_blank" >http://dx.doi.org/10.1137/1.9781611973402.14</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/1.9781611973402.14" target="_blank" >10.1137/1.9781611973402.14</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 to Rn on a finite simplicial complex K and alpha>0, it holds that each function g:K to Rn 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 <= 2n3. 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 >= 2n2, 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 piecewise linear. Such functions can approximate general continuous functions, and thus we get approximation schemes and undecidability of the robust satisfiability in other possib
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
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
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms
ISBN
978-1-61197-338-9
ISSN
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e-ISSN
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Number of pages
11
Pages from-to
193-203
Publisher name
SIAM
Place of publication
Philadelphia
Event location
Portland
Event date
Jan 5, 2014
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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