Full discretization of distributed control problems for parabolic equations

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

• Documents
• Education
• Cours
• Hubert
• Équation
• Aix-Marseille Université
• multiplication
• mathématiques
• mathématique
• Mathématiques

Informations

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

Exrait

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]