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

By Lothar Reichel

Appears in 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.

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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

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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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