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Topics in structured linear algebra - lecture 2
Virtualconference
Authors : Boito, Paola (Author of the conference)
CIRM (Publisher )
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
Additional resources :
https://www.cirm-math.fr/RepOrga/2564/Slides/01_slidesBoito.pdf
CIRM (Publisher )
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Abstract :
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
MSC Codes : 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
Additional resources :
https://www.cirm-math.fr/RepOrga/2564/Slides/01_slidesBoito.pdf
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 19/03/2021 Conference Date : 02/03/2021 Subseries : Research School arXiv category : Numerical Analysis Mathematical Area(s) : Numerical Analysis & Scientific Computing Format : MP4 (.mp4) - HD Video Time : 01:43:33 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2021-03-02_Boito_2.mp4 
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Information on the Event
Event Title : French Computer Algebra Days / JNCF - Journées nationales de calcul formelEvent Organizers : Bardet, Magali ; Busé, Laurent ; Koseleff, Pierre-Vincent ; Vaccon, Tristan Dates : 01/03/2021 - 05/03/2021 Event Year : 2021 Event URL : https://conferences.cirm-math.fr/2564.html
Citation Data
DOI : 10.24350/CIRM.V.19722403Cite this video as: Boito, Paola (2021). Topics in structured linear algebra - lecture 2. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19722403 URI : http://dx.doi.org/10.24350/CIRM.V.19722403 |
See Also
- [Virtualconference] Computational real algebraic geometry and applications to robotics - lecture 2 / Author of the conference Moroz, Guillaume.
- [Virtualconference] Complexity of Gröbner bases computations and applications to cryptography - lecture 2 / Author of the conference Gorla, Elisa.
- [Virtualconference] Tree-indexed polynomials and power series - lecture 2 / Author of the conference Chapoton, Frédéric.
- [Virtualconference] Computational real algebraic geometry and applications to robotics - lecture 1 / Author of the conference Moroz, Guillaume.
- [Virtualconference] Complexity of Gröbner bases computations and applications to cryptography - lecture 1 / Author of the conference Gorla, Elisa.
- [Virtualconference] Combinatorics and algebra of partially ordered sets - lecture 1 / Author of the conference Chapoton, Frédéric.
- [Virtualconference] Topics in structured linear algebra - lecture 1 / Author of the conference Boito, Paola.
Bibliography
- 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. -
