Full discretization of distributed control problems for parabolic equations

Franck Boyer

Description

Full discretization of distributed control problems for parabolic equations Franck BOYER? joint work with Florence HUBERT? and Jerome LE ROUSSEAU† ? LATP, Aix-Marseille Universite †MAPMO, Universite d'Orleans IHP, November 2010 1/ 58 F. Boyer Control of full-discrete parabolic equations

• control problem


• equations


• aix-marseille universite


• full-discrete parabolic


• time discretization schemes

Sujets

• Hubert
• Équation
• Aix-Marseille Université
• multiplication
• mathématiques
• mathématique
• Mathématiques

Informations

• Publié par: pefav
• Nombre de lectures: 23
• Langue: English

Extrait

Motivation Factorization of cyclotomic polynomials Some steps to abelian extensions Conclusion

polynomials over finite nisticopylimenomial-t

Factorization of determi

Ivan Boyer

Doctorant sous la direction de Jean-François Mestre Institut Mathématique de Jussieu

AGCT-13 — C.I.R.M. March 15, 2011

I. Boyer

Factorization inF p [X]

fields

in

Motivation Factorization of cyclotomic polynomials Some steps to abelian extensions Conclusion Algorithmic aspect.

Context Schoof’s algorithm

Remark Thedeterministicaspect iscrucialin this talk : everything be- comes “trivial” in probabilistic time. In the same way, assuming G.R.H. would withdraw some of the interest of the following !

I. Boyer

Factorization in

F p [

X]

Motivation Factorization of cyclotomic polynomialsContext Some steps to abelian extensionsSchoof’s algorithm Conclusion Factorization inF p [X]– Square roots in

F p .

I There are deterministic algorithms inF p [X](egBerlekamp’s algorithm) but exponential in logp. I No deterministic polynomial-time algorithm is known for factorization inF p [X]. Even in degree 2 ! I Easy to decide ifa∈F p is a square (Legendre symbol, or more generally the g.c.d. withx p −x) I A lot of literature for square root probabilistic-algorithms, but as for now, we don’t know if it’s aP–problem. I However, thanks toSchoof’s algorithm, we can say some- thing indeterministictime.

I. Boyer

Factorization inF p [X]

Motivation Factorization of cyclotomic polynomialsContext Some steps to abelian extensionsSchoof’s algorithm Conclusion Factorization inF p [X]– Square roots in

I

I

I

I

I

F p .

There are deterministic algorithms inF p [X](egBerlekamp’s algorithm) but exponential in logp. No deterministic polynomial-time algorithm is known for factorization inF p [X] in degree 2 !. Even Easy to decide ifa∈F p is a square (Legendre symbol, or more generally the g.c.d. withx p −x) A lot of literature for square root probabilistic-algorithms, but as for now, we don’t know if it’s aP–problem. However, thanks toSchoof’s algorithm, we can say some- thing indeterministictime.

I. Boyer

Factorization inF p [X]

Motivation Factorization of cyclotomic polynomialsContext Some steps to abelian extensionsSchoof’s algorithm Conclusion Factorization inF p [X]– Square roots in

I

I

I

I

I

F p

.

There are deterministic algorithms inF p [X](egBerlekamp’s algorithm) but exponential in logp. No deterministic polynomial-time algorithm is known for factorization inF p [X]. Even in degree 2 ! Easy to decide ifa∈F p is a square (Legendre symbol, or more generally the g.c.d. withx p −x) A lot of literature for square root probabilistic-algorithms, but as for now, we don’t know if it’s aP–problem. However, thanks toSchoof’s algorithm, we can say some- thing indeterministictime.

I. Boyer

Factorization inF p [X]

Motivation Factorization of cyclotomic polynomialsContext Some steps to abelian extensionsSchoof’s algorithm Conclusion Factorization inF p [X]– Square roots in

I

I

I

I

I

F p

.

There are deterministic algorithms inF p [X](egBerlekamp’s algorithm) but exponential in logp. No deterministic polynomial-time algorithm is known for factorization inF p [X]. Even in degree 2 ! Easy to decide ifa∈F p is a square (Legendre symbol, or more generally the g.c.d. withx p −x) A lot of literature for square root probabilistic-algorithms, but as for now, we don’t know if it’s aP–problem. However, thanks toSchoof’s algorithm, we can say some- thing indeterministictime.

I. Boyer

Factorization inF p [X]