Real root finding for low rank linear matrices
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F20%3A00340150" target="_blank" >RIV/68407700:21230/20:00340150 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s00200-019-00396-w" target="_blank" >https://doi.org/10.1007/s00200-019-00396-w</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00200-019-00396-w" target="_blank" >10.1007/s00200-019-00396-w</a>
Alternative languages
Result language
angličtina
Original language name
Real root finding for low rank linear matrices
Original language description
We consider mx s matrices (with m>= s) in a real affine subspace of dimension n. The problem of finding elements of low rank in such spaces finds many applications in information and systems theory, where low rank is synonymous of structure and parsimony. We design computer algebra algorithms, based on advanced methods for polynomial system solving, to solve this problem efficiently and exactly: the input are the rational coefficients of the matrices spanning the affine subspace as well as the expected maximum rank, and the output is a rational parametrization encoding a finite set of points that intersects each connected component of the low rank real algebraic set. The complexity of our algorithm is studied thoroughly. It is polynomial in (n+m(s-r)n). It improves on the state-of-the-art in computer algebra and effective real algebraic geometry. Moreover, computer experiments show the practical efficiency of our approach.
Czech name
—
Czech description
—
Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10100 - Mathematics
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Applicable Algebra in Engineering, Communication and Computing
ISSN
0938-1279
e-ISSN
1432-0622
Volume of the periodical
31
Issue of the periodical within the volume
2
Country of publishing house
US - UNITED STATES
Number of pages
33
Pages from-to
101-133
UT code for WoS article
000518201000002
EID of the result in the Scopus database
2-s2.0-85069658735