Numerical Methods and Scientific Computing / Méthodes numériques et calcul scientifique

Collection Numerical Methods and Scientific Computing / Méthodes numériques et calcul scientifique

Organizer(s) Beckermann, Bernhard ; Brezinski, Claude ; da Rocha, Zélia ; Redivo-Zaglia, Michela ; Rodriguez, Giuseppe

Date(s) 08/11/2021 - 12/11/2021

linked URL https://conferences.cirm-math.fr/2431.html

00:00:00 / 00:00:00

5 5

Approximation of Stieltjes matrix functions by rational Gauss-type quadrature rules

By Lothar Reichel

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.

Information about the video

Date of recording 09/11/2021
Date of publication 26/11/2021
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Luca Recanzone
Format MP4

Citation data

DOI 10.24350/CIRM.V.19829603
Cite this video Reichel, Lothar (09/11/2021). Approximation of Stieltjes matrix functions by rational Gauss-type quadrature rules. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19829603
URL https://dx.doi.org/10.24350/CIRM.V.19829603

Domain(s)

Numerical Analysis

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

MSC codes

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