Detecting rigid convexity of bivariate polynomials

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F10%3A00160536" target="_blank" >RIV/68407700:21230/10:00160536 - isvavai.cz</a>
Result on the web
—
DOI - Digital Object Identifier
—

Result language
angličtina
Original language name
Detecting rigid convexity of bivariate polynomials
Original language description
Given a polynomial x in Rn -> p(x) in n = 2 variables, a symbolicnumerical algorithm is first described for detecting whether the connected component of the plane sublevel set P = {x : p(x) 0} containing the origin is rigidly convex, or equivalently, whether it has a linear matrix inequality (LMI) representation, or equivalently, if polynomial p(x) is hyperbolic with respect to the origin. The problem boils down to checking whether a univariate polynomial matrix is positive semidefinite, an optimizationproblem that can be solved with eigenvalue decomposition. When the variety C = {x : p(x) = 0} is an algebraic curve of genus zero, a second algorithm based on Be´ zoutians is proposed to detect whether P has an LMI representation and to build such a representation from a rational parametrization of C. Finally, some extensions to positive genus curves and to the case n > 2 are mentioned.
Czech name
—
Czech description
—

Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—

Project
<a href="/en/project/GA102%2F08%2F0186" target="_blank" >GA102/08/0186: Algorithms for Complex Systems Analysis and Control Design</a><br>
Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2010
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)