Robust Satisfiability of Systems of Equations

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Robust Satisfiability of Systems of Equations

Popis výsledku v původním jazyce

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

Název v anglickém jazyce

Robust Satisfiability of Systems of Equations

Popis výsledku anglicky

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

Druh

D - Stať ve sborníku

CEP obor

IN - Informatika

OECD FORD obor

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Projekt

<a href="/cs/project/GBP202%2F12%2FG061" target="_blank" >GBP202/12/G061: Centrum excelence - Institut teoretické informatiky (CE-ITI)</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2014

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

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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Počet stran výsledku

11

Strana od-do

193-203

Název nakladatele

SIAM

Místo vydání

Philadelphia

Místo konání akce

Portland

Datum konání akce

5. 1. 2014

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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