About: Detecting rigid convexity of bivariate polynomials

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	Given a polynomial x ∈ 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 optimization problem 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. Given a polynomial x ∈ 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 optimization problem 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. (en)
Title	Detecting rigid convexity of bivariate polynomials Detecting rigid convexity of bivariate polynomials (en)
skos:prefLabel	Detecting rigid convexity of bivariate polynomials Detecting rigid convexity of bivariate polynomials (en)
skos:notation	RIV/68407700:21230/10:00160536!RIV11-GA0-21230___
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(GA102/08/0186), Z(MSM6840770038)
http://linked.open...iv/cisloPeriodika	5
http://linked.open...vai/riv/dodaniDat	2011
http://linked.open...aciTvurceVysledku	Henrion, Didier
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	České vysoké učení technické v Praze / Fakulta elektrotechnická
http://linked.open...dnocenehoVysledku	253625
http://linked.open...ai/riv/idVysledku	RIV/68407700:21230/10:00160536
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Multivariate polynomials; Convexity; Linear matrix inequality; Real algebraic geometry (en)
http://linked.open.../riv/klicoveSlovo	Real algebraic geometry Convexity Linear matrix inequality Multivariate polynomials
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[87104096374E]
http://linked.open...i/riv/nazevZdroje	Linear Algebra and Its Applications
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	1 (xsd:int)
http://linked.open...vavai/riv/projekt	Algorithms for Complex Systems Analysis and Control Design
http://linked.open...UplatneniVysledku	2010
http://linked.open...v/svazekPeriodika	432
http://linked.open...iv/tvurceVysledku	Henrion, Didier
http://linked.open...ain/vavai/riv/wos	000274460300009
http://linked.open...n/vavai/riv/zamer	Decision Making and Control for Manufacturing III
issn	0024-3795
number of pages	16 (xsd:int)
http://localhost/t...ganizacniJednotka	21230
is http://linked.open...avai/riv/vysledek of	Detecting rigid convexity of bivariate polynomials

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