Convergence analysis and parameter choice for the iterated Arnoldi-Tikhonov method | Vidéo | Carmin.tv

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

De Lothar Reichel

Apparaît dans la collection : Numerical Linear Algebra / Algèbre Linéaire Numérique

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.

Informations sur la vidéo

Date de captation 16/09/2024
Date de publication 07/10/2024
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Audience Chercheurs, Doctorants
Réalisateur(s) Guillaume Hennenfent
Format MP4

Données de citation

DOI 10.24350/CIRM.V.20246403
Citer cette vidéo 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

Domaine(s)

Analyse numérique

Bibliographie

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

Codes MSC

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