• D

F Nous contacter

0

# Multi angle

O

Multi angle Condition: the geometry of numerical algorithms - Lecture 2

Auteurs : Bürgisser, Peter (Auteur de la Conférence)
CIRM (Editeur )

Résumé : The performance of numerical algorithms, both regarding stability and complexity, can be understood in a unified way in terms of condition numbers. This requires to identify the appropriate geometric settings and to characterize condition in geometric ways.
A probabilistic analysis of numerical algorithms can be reduced to a corresponding analysis of condition numbers, which leads to fascinating problems of geometric probability and integral geometry. The most well known example is Smale's 17th problem, which asks to find a solution of a given system of n complex homogeneous polynomial equations in $n$ + 1 unknowns. This problem can be solved in average (and even smoothed) polynomial time.
In the course we will explain the concepts necessary to state and solve Smale's 17th problem. We also show how these ideas lead to new numerical algorithms for computing eigenpairs of matrices that provably run in average polynomial time. Making these algorithms more efficient or adapting them to structured settings are challenging and rewarding research problems. We intend to address some of these issues at the end of the course.

Codes MSC :
15A12 - Conditioning of matrices
65F10 - Iterative methods for linear systems
65F35 - Matrix norms, conditioning, scaling (numerical linear algebra)
65H10 - Systems of equations
65K05 - Mathematical programming methods
68Q15 - Complexity classes (hierarchies, relations among complexity classes, etc.)
90C51 - Interior-point methods

 Informations sur la Vidéo Réalisateur : Hennenfent, Guillaume Langue : Anglais Date de publication : 26/01/17 Date de captation : 17/01/17 Collection : Research talks Format : MP4 Durée : 01:32:30 Domaine : Computer Science ; Numerical Analysis & Scientific Computing Audience : Chercheurs ; Doctorants , Post - Doctorants Download : http://videos.cirm-math.fr/2017-01-17_Burgisser_Part2.mp4 Informations sur la rencontre Nom du congrès : French computer algebra days / Journées nationales de calcul formelOrganisteurs Congrès : Brisebarre, Nicolas ; El Bacha, Carole ; Giorgi, Pascal ; Mezzarobba, Marc ; Moroz, GuillaumeDates : 16/01/17 - 20/01/17 Année de la rencontre : 2017 URL Congrès : http://conferences.cirm-math.fr/1584.htmlCitation DataDOI : 10.24350/CIRM.V.19110503Cite this video as: Bürgisser, Peter (2017). Condition: the geometry of numerical algorithms - Lecture 2. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19110503URI : http://dx.doi.org/10.24350/CIRM.V.19110503

### Voir aussi

Bibliographie

1. Bürgisser, P., Cucker, F. (2013). Condition. The geometry of numerical algorithms. Berlin: Springer - http://dx.doi.org/10.1007/978-3-642-38896-5

Z