English
Topics in structured linear algebra - lecture 1
Virtualconference
Auteurs : Boito, Paola (Auteur de la Conférence)
CIRM (Editeur )
65F15 - Eigenvalues, eigenvectors
65F60 - Matrix exponential and similar matrix functions (numerical linear algebra) - Numerical computation of matrix exponential and similar matrix functions
15B99 - Special matrices
Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/2564/Slides/01_slidesBoito.pdf
CIRM (Editeur )
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Résumé :
Structure is a fundamental concept in linear algebra: matrices arising from applications often inherit a special form from the original problem, and this special form can be analysed and exploited to design efficient algorithms. In this short course we will present some examples of matrix structure and related applications. Here we are interested in data-sparse structure, that is, structure that allows us to represent an n × n matrix using only O(n) parameters. One notable example is provided by quasi separable matrices, a class of (generally dense) rank-structured matrices where off-diagonal blocks have low rank.
We will give an overview of the properties of these structured classes and present a few examples of how algorithms that perform basic tasks – e.g., solving linear systems, computing eigenvalues, approximating matrix functions – can be tailored to specific structures.
Keywords : structured matrices; eigenvalue computation; functions of matrices
Codes MSC : We will give an overview of the properties of these structured classes and present a few examples of how algorithms that perform basic tasks – e.g., solving linear systems, computing eigenvalues, approximating matrix functions – can be tailored to specific structures.
Keywords : structured matrices; eigenvalue computation; functions of matrices
65F15 - Eigenvalues, eigenvectors
65F60 - Matrix exponential and similar matrix functions (numerical linear algebra) - Numerical computation of matrix exponential and similar matrix functions
15B99 - Special matrices
Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/2564/Slides/01_slidesBoito.pdf
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 19/03/2021 Date de captation : 02/03/2021 Sous collection : Research School arXiv category : Numerical Analysis Domaine : Numerical Analysis & Scientific Computing Format : MP4 (.mp4) - HD Durée : 01:39:42 Audience : Researchers Download : https://videos.cirm-math.fr/2021-03-01_Boito_1.mp4 
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Informations sur la Rencontre
Nom de la rencontre : French Computer Algebra Days / JNCF - Journées nationales de calcul formelOrganisateurs de la rencontre : Bardet, Magali ; Busé, Laurent ; Koseleff, Pierre-Vincent ; Vaccon, Tristan Dates : 01/03/2021 - 05/03/2021 Année de la rencontre : 2021 URL Congrès : https://conferences.cirm-math.fr/2564.html
Données de citation
DOI : 10.24350/CIRM.V.19718703Citer cette vidéo: Boito, Paola (2021). Topics in structured linear algebra - lecture 1. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19718703 URI : http://dx.doi.org/10.24350/CIRM.V.19718703 |
Voir aussi
- [Virtualconference] Computational real algebraic geometry and applications to robotics - lecture 2 / Auteur de la Conférence Moroz, Guillaume.
- [Virtualconference] Complexity of Gröbner bases computations and applications to cryptography - lecture 2 / Auteur de la Conférence Gorla, Elisa.
- [Virtualconference] Tree-indexed polynomials and power series - lecture 2 / Auteur de la Conférence Chapoton, Frédéric.
- [Virtualconference] Topics in structured linear algebra - lecture 2 / Auteur de la Conférence Boito, Paola.
- [Virtualconference] Computational real algebraic geometry and applications to robotics - lecture 1 / Auteur de la Conférence Moroz, Guillaume.
- [Virtualconference] Complexity of Gröbner bases computations and applications to cryptography - lecture 1 / Auteur de la Conférence Gorla, Elisa.
- [Virtualconference] Combinatorics and algebra of partially ordered sets - lecture 1 / Auteur de la Conférence Chapoton, Frédéric.
Bibliographie
- AURENTZ, Jared L., MACH, Thomas, ROBOL, Leonardo, et al. Core-chasing algorithms for the eigenvalue problem. Society for Industrial and Applied Mathematics, 2018. -
- BOITO, Paola, EIDELMAN, Yuli, et GEMIGNANI, Luca. Implicit QR for companion-like pencils. Mathematics of Computation, 2016, vol. 85, no 300, p. 1753-1774. - https://doi.org/10.1090/mcom/3020
- BOITO, Paola, EIDELMAN, Yuli, et GEMIGNANI, Luca. Efficient solution of parameter‐dependent quasiseparable systems and computation of meromorphic matrix functions. Numerical Linear Algebra with Applications, 2018, vol. 25, no 6, p. e2141. - https://doi.org/10.1002/nla.2141
- EIDELMAN, Yuli, GOHBERG, Israel, et HAIMOVICI, Iulian. Separable type representations of matrices and fast algorithms. Birkhäuser, Vol 1& 2 , 2014. - http://dx.doi.org/10.1007/978-3-0348-0606-0
- HIGHAM, Nicholas J. Functions of matrices: theory and computation. Society for Industrial and Applied Mathematics, 2008. - https://doi.org/10.1137/1.9780898717778
- VANDEBRIL, Raf, VAN BAREL, Marc, et MASTRONARDI, Nicola. Matrix computations and semiseparable matrices: linear systems. JHU Press, 2007. -
