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Approximation of Stieltjes matrix functions by rational Gauss-type quadrature rules
Multi angle
Authors : Reichel, Lothar (Author of the conference)
CIRM (Publisher )
65D15 - Algorithms for functional approximation
65D32 - Quadrature and cubature formulas
65F20 - Overdetermined systems, pseudoinverses
CIRM (Publisher )
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Abstract :
This talk is concerned with the inexpensive approximation of expressions of the form $I(f)=$ $v^{T} f(A) v$, when $A$ is a large symmetric positive definite matrix, $v$ is a vector, and $f(t)$ is a Stieltjes function. We are interested in the situation when $A$ is too large to make the evaluation of $f(A)$ practical. Approximations of $I(f)$ are computed with the aid of rational Gauss quadrature rules. Error bounds or estimates of bounds are determined with rational Gauss-Radau or rational anti-Gauss rules.
Keywords : Stieltjes function; rational Gauss quadrature
MSC Codes : Keywords : Stieltjes function; rational Gauss quadrature
65D15 - Algorithms for functional approximation
65D32 - Quadrature and cubature formulas
65F20 - Overdetermined systems, pseudoinverses
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Information on the Video
Film maker : Récanzone, LucaLanguage : English Available date : 26/11/2021 Conference Date : 09/11/2021 Subseries : Research talks arXiv category : Numerical Analysis Mathematical Area(s) : Numerical Analysis & Scientific Computing Format : MP4 (.mp4) - HD Video Time : 00:27:28 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2021-11-09_Reichel.mp4 
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Information on the Event
Event Title : Numerical Methods and Scientific Computing / Méthodes numériques et calcul scientifiqueEvent Organizers : Beckermann, Bernhard ; Brezinski, Claude ; da Rocha, Zélia ; Redivo-Zaglia, Michela ; Rodriguez, Giuseppe Dates : 08/11/2021 - 12/11/2021 Event Year : 2021 Event URL : https://conferences.cirm-math.fr/2431.html
Citation Data
DOI : 10.24350/CIRM.V.19829603Cite this video as: Reichel, Lothar (2021). Approximation of Stieltjes matrix functions by rational Gauss-type quadrature rules. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19829603 URI : http://dx.doi.org/10.24350/CIRM.V.19829603 |
See Also
- [Multi angle] Gauss's Gaussian quadrature / Author of the conference Sanz-Serna, Jesús María.
- [Multi angle] Subspace iteration and variants, revisited / Author of the conference Saad, Yousef.
- [Multi angle] Detection and correction of silent errors in the Conjugate Gradient algorithm / Author of the conference Meurant, Gérard.
- [Multi angle] On the invention of iterative methods for linear systems / Author of the conference Gander, Martin.
Bibliography
- FROMMER, Andreas et SCHWEITZER, Marcel. Error bounds and estimates for Krylov subspace approximations of Stieltjes matrix functions. BIT Numerical Mathematics, 2016, vol. 56, no 3, p. 865-892. - http://dx.doi.org/10.1007/s10543-015-0596-3
- GOLUB, Gene H. et MEURANT, Gérard. Matrices, moments and quadrature with applications. Princeton University Press, 2009. - https://doi.org/10.1515/9781400833887
- PRANIC, Miroslav S. et REICHEL, Lothar. Rational Gauss quadrature. SIAM Journal on Numerical Analysis, 2014, vol. 52, no 2, p. 832-851. - https://doi.org/10.1137/120902161
