Real root finding for determinants of linear matrices
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F16%3A00234174" target="_blank" >RIV/68407700:21230/16:00234174 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.jsc.2015.06.010" target="_blank" >http://dx.doi.org/10.1016/j.jsc.2015.06.010</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jsc.2015.06.010" target="_blank" >10.1016/j.jsc.2015.06.010</a>
Alternative languages
Result language
angličtina
Original language name
Real root finding for determinants of linear matrices
Original language description
Let A0, A1, ..., Anbe given square matrices of size mwith rational coefficients. The paper focuses on the exact computation of one point in each connected component of the real determinantal vari-ety {x elementRn:det(A0+x1A1+...+xnAn) =0}. Such a problem finds applications in many areas such as control theory, computational geometry, optimization, etc. Under some genericity assumptions on the coefficients of the matrices, we provide an algorithm solving this problem whose runtime is essentially polynomial in the bino-mial coefficient n+mn. We also report on experiments with a com-puter implementation of this algorithm. Its practical performance illustrates the complexity estimates. In particular, we emphasize that for subfamilies of this problem where mis fixed, the com-plexity is polynomial inn.
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
BA - General mathematics
OECD FORD branch
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Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2016
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 Symbolic Computation
ISSN
0747-7171
e-ISSN
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Volume of the periodical
74
Issue of the periodical within the volume
May-June
Country of publishing house
GB - UNITED KINGDOM
Number of pages
34
Pages from-to
205-238
UT code for WoS article
000366794100011
EID of the result in the Scopus database
2-s2.0-84948720100