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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 ...
65F35 ; 65K05 ; 68Q15 ; 68W01 ; 15A12 ; 65F10 ; 90C51 ; 65H10
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- 256 p.
ISBN 978-0-8218-2892-2
DIMACS series in discrete mathematics and theorerical computer science , 0059
Localisation : Collection 1er étage
informatique # structure de données # algorithme # recherche # tri # géométrie assistée par ordinateur # évaluation de performance # priorité # queue # plus proche voisin # recherche d'information # WAB # ADN # image
68-06 ; 68P05 ; 68P10 ; 68Uxx ; 68W01
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- 306 p.
ISBN 978-0-8218-1184-9
DIMACS series in discrete mathematics and theoretical computer science , 0050
Localisation : Collection 1er étage
algorithme de calcul # algorithme numérique # algorithmique # algèbre numérique # calcul des algorithmes numériques # calcul parallèle # complexité des algorithmes # gestion de mémoire # infographie # informatique théorique # mathématique discrète # modèle de calcul # structure des données # traitement des données
65Fxx ; 65Y20 ; 68Pxx ; 68Q05 ; 68Q25 ; 68R01 ; 68R10 ; 68U05 ; 68W01 ; 68W40
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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 ...
65F35 ; 65K05 ; 68Q15 ; 68W01 ; 15A12 ; 65F10 ; 90C51 ; 65H10
... Lire [+]
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- 341 p.
ISBN 978-0-8218-2815-1
Fields institute monographs , 0019
Localisation : Collection 1er étage;Réserve
combinatoire # informatique # théorie des graphes # algorithme # représentation des graphes # complexité # optimisation
05-02 ; 68-01 ; 68R10 ; 68W01
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- x; 219 p.
ISBN 978-0-691-14714-7
Localisation : Ouvrage RdC (MACC)
intelligence artificielle # algorithme # informatique # moteur de recherche # index # Google # reconnaissance de motifs # vulgarisation # cryptage
68-01 ; 68W01 ; 00A09 ; 68P25 ; 68P30 ; 68U35
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- xxv; 723 p.
ISBN 978-0-07-127524-8
Localisation : Ouvrage RdC (INTR)
algorithmes # complexité # programmation dynamique # arbre # stratégie
68W01 ; 68-01
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