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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

  • Czech description

Classification

  • Type

    J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

  • CEP classification

    BA - General mathematics

  • OECD FORD branch

Result continuities

  • Project

  • 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

  • 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