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# Documents  90C51 | enregistrements trouvés : 7

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

Post-edited

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 ...

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

Multi angle

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 ...

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## Condition: the geometry of numerical algorithms Bürgisser, Peter ; Cucker, Felipe | Springer 2013

Ouvrage

- xxxi; 554 p.
ISBN 978-3-642-38895-8

Grundlehren der mathematischen wissenschaften , 0349

Localisation : Collection 1er étage

analyse numérique # algorithme # nombre de conditionnement # algèbre linéaire # optimisation linéaire # résolution d'équation polynômiale # analyse d'erreur # système linéaire triangulaire # algorithme itératif pour résolution d'équation linéaire # méthode des ellipsoides # méthode des points intérieurs # analyse probabilistique de nombre conditionnel # méthode de Newton # 17ème problème de Smale

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## Convex analysis and nonlinear optimization :theory and examples Borwein, Jonathan ; Lewis, Adrian S. | Springer 2006

Ouvrage

- 310 p.
ISBN 978-0-387-29570-1

CMS Books in mathematics

Localisation : Ouvrage RdC (BORW)

fonction convexe # optimisation # théorie non-linéaire # calcul de variations # point intérieur # programmation convexe # dualité de Frenckel # théorème de Karush-Kuhn-Tucker # point fixe # théorème de Radenacker

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## Optimisation numérique :aspects théoriques et pratiques Bonnans, J. Frédéric ; Gilbert, Jean Charles ; Lemaréchal, Claude ; Sagastizabal, Claudia | Springer;Société de Mathématiques Appliquées et Industrielles 1997

Ouvrage

- vii; 324 p.
ISBN 978-3-540-63183-5

Mathématiques & applications , 0027

Localisation : Collection 1er étage

algorithme optimal # programmation linéaire # programmation quadratique # programmation non linéaire # programmation avec contraintes # processus stochastique # optimisation numérique # méthode de points intérieurs # optimisation non contrainte # programmation non différentiable # méthode de Newton

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## Optimization - theory and practice Forst, Wilhelm ; Hoffmann, Dieter | Springer 2010

Ouvrage

- xviii; 402 p.
ISBN 978-0-387-78976-7

Springer undergraduate texts in mathematics and technology

Localisation : Ouvrage RdC (FORS)

optimisation # programmation mathématique

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## Polyhedral and semidefinite programming methods in combinatorial optimization Tunçel, Levent | American Mathematical Society;The Fields Institute for Research in Mathematical Sciences 2010

Ouvrage

- x; 219 p.
ISBN 978-0-8218-3352-0

Fields institute monographs , 0027

Localisation : Collection 1er étage

programmation semidéfinie # optmisation combinatoire # optimisation combinatoire # inégalité linéaire de matrices # géométrie convexe

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