Numerical Linear Algebra / Algèbre Linéaire Numérique

Collection Numerical Linear Algebra / Algèbre Linéaire Numérique

Organizer(s) Brezinski, Claude ; Chehab, Jean-Paul ; Redivo-Zaglia, Michela ; Rodriguez, Giuseppe ; Sadok, Hassane

Date(s) 16/09/2024 - 20/09/2024

linked URL https://conferences.cirm-math.fr/3064.html

00:00:00 / 00:00:00

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Convergence analysis and parameter choice for the iterated Arnoldi-Tikhonov method

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 16/09/2024
Date of publication 07/10/2024
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.20246403
Cite this video Reichel, Lothar (16/09/2024). Convergence analysis and parameter choice for the iterated Arnoldi-Tikhonov method. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20246403
URL https://dx.doi.org/10.24350/CIRM.V.20246403

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, 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.
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

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