On the permissible arrangements of Ritz values for normal matrices in the complex plane (CROSBI ID 189736)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
Podaci o odgovornosti
Bujanović, Zvonimir
engleski
On the permissible arrangements of Ritz values for normal matrices in the complex plane
This article discusses Ritz and harmonic Ritz values computed from a Krylov subspace, generated by a normal matrix. We give necessary and sufficient conditions for a given tuple of complex numbers to represent Ritz values: the existence of a positive solution to a certain linear system with Cauchy matrix. Using this characterization, we prove several localization results for the Ritz values of normal matrices and discuss consequences for the convergence of the restarted Arnoldi algorithm. Similar results are shown for the harmonic case as well.
eigenvalues ; Ritz values ; harmonic Ritz values ; Krylov subspaces ; Arnoldi algorithm
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Podaci o izdanju
438 (12)
2013.
4606-4624
objavljeno
0024-3795
1873-1856
10.1016/j.laa.2013.02.014