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Topics in structured linear algebra - lecture 2

Apparaît dans la collection : 2021 - French computer algebra days / Journées nationales de calcul formel

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.

Informations sur la vidéo

Date de captation 02/03/2021
Date de publication 19/03/2021
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Audience Chercheurs
Réalisateur(s) Guillaume Hennenfent
Format MP4

Données de citation

DOI 10.24350/CIRM.V.19722403
Citer cette vidéo Boito, Paola (02/03/2021). Topics in structured linear algebra - lecture 2. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19722403
URL https://dx.doi.org/10.24350/CIRM.V.19722403

Domaine(s)

Analyse numérique

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. -

Codes MSC

Document(s)

https://www.cirm-math.fr/RepOrga/2564/Slides/01_slidesBoito.pdf

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