Root finding with threshold circuits

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F12%3A00382374" target="_blank" >RIV/67985840:_____/12:00382374 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.tcs.2012.09.001" target="_blank" >http://dx.doi.org/10.1016/j.tcs.2012.09.001</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.tcs.2012.09.001" target="_blank" >10.1016/j.tcs.2012.09.001</a>

Result language
angličtina
Original language name
Root finding with threshold circuits
Original language description
We show that for any constant d, complex roots of degree d univariate rational (or Gaussian rational) polynomials---given by a list of coefficients in binary---can be computed to a given accuracy by a uniform TC^0 algorithm (a uniform family of constant-depth polynomial-size threshold circuits). The basic idea is to compute the inverse function of the polynomial by a power series. We also discuss an application to the theory VTC^0 of bounded arithmetic.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2012
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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