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# Documents  Brisebarre, Nicolas | enregistrements trouvés : 4

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## Condition: the geometry of numerical algorithms - Lecture 1 Bürgisser, Peter | CIRM H

Post-edited

Research talks;Computer Science

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.
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 ...

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Condition: the geometry of numerical algorithms - Lecture 2 Bürgisser, Peter | CIRM H

Multi angle

Research talks;Computer Science

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.
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 ...

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Handbook of floating-point arithmetic Muller, Jean-Michel ; Brisebarre, Nicolas ; de Dinechin,Florent ; Jeannerod, Claude-Pierre ; Lefèvre, Vincent ; Melquiond, Guillaume ; Revol, Nathalie ; Stehlé, Damien ; Torres, Serge | Birkhäuser 2010

Ouvrage

- xxiii; 572 p.
ISBN 978-0-8176-4704-9

Localisation : Ouvrage RdC (HAND)

Arithmétique à virgule flottante # langage de programmation # nombre à virgule flottante # algorithme # implémentation logicielle # implémentation matérielle # compilateur

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## Une étude de deux problèmes diophantiens Brisebarre, Nicolas | Université de Bordeaux I 1998

Thèse

- 107 p.

Localisation : Ouvrage RdC (BRIS)

algorithmique # approximation diophantienne # équations aux différences # équations différentielles linéaires # mesures d'irrationalité # polynômes # polynômes exponentiels

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