Naslov
On the condition behaviour in the Jacobi method
(On the condition behaviour in the Jacobi Method)

Autori
Drmač, Zlatko

Izvornik
SIAM journal on matrix analysis and applications (0895-4798) 17 (1996), 3; 509-514

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Jacobi methods ; accuracy ; condition behaviour ; optimal scaling

Sažetak
The aim of this note is to show that the matrix $S(n, \alpha)=(1-\alpha)I+\alpha ee^T$, $e=(1, \ldots, 1)^T$, $\alpha\in(0, 1)$ is not a counterexample for the accuracy properties of the Jacobi method for computing the singular and eigenvalue decomposition, as might be nderstood from a recent article of Mascarenhas in this journal. In fact, the Jacobi process on $S(n, \alpha)$ is an example of the perfect behaviour of the algorithm. It is shown that Jacobi rotations preserve the optimal (with respect to diagonal scalings) spectral condition number of $S(n, \alpha)$.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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