2017 - French computer algebra days - Journées nationales de calcul formel

Collection 2017 - French computer algebra days - Journées nationales de calcul formel

Organisateur(s) Nicolas Brisebarre (ENS Lyon) Carole El Bacha (Université Libanaise, Fanar) Pascal Giorgi (Université de Montpellier) Marc Mezzarobba (Université Pierre et Marie Curie) Guillaume Moroz (INRIA Nancy Grand Est)

Date(s) 16/01/2017 - 20/01/2017

URL associée https://conferences.cirm-math.fr/1584.html

00:00:00 / 00:00:00

2 2

Chapitres

Condition: the geometry of numerical algorithms - Lecture 1

De Peter Bürgisser

Apparaît également dans la collection : Exposés de recherche

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.

Informations sur la vidéo

Date de captation 16/01/2017
Date de publication 26/01/2017
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Réalisateur(s) Guillaume Hennenfent
Format MP4

Données de citation

DOI 10.24350/CIRM.V.19110103
Citer cette vidéo Bürgisser, Peter (16/01/2017). Condition: the geometry of numerical algorithms - Lecture 1. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19110103
URL https://dx.doi.org/10.24350/CIRM.V.19110103

Domaine(s)

Bibliographie

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

Codes MSC

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