Naslov
Globally convergent Jacobi methods for positive definite matrix pairs

Autori
Hari, Vjeran

Izvornik
Numerical algorithms (1017-1398) 79 (2018), 1; 221-249

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

Ključne riječi
Generalized eigenvalue problem ; Jacobi method ; Global convergence

Sažetak
The paper derives and investigates Jacobi methods for the generalized eigenvalue problem $Ax=\lambda Bx$, where $A$ is symmetric and $B$ is symmetric positive definite matrix. The methods first ``normalize'' $B$ to have unit diagonal and then maintain that property during the iterative process. The global convergence is proved for all such methods. The result is obtained for the large class of generalized serial strategies from Hari and Begović-Kovač (Trans. Numer. Anal. (ETNA). Preliminary numerical tests confirm high relative accuracy of some of those methods provided that the both matrices are positive definite and the spectral condition numbers of $\Delta_AA\Delta_A$ and $\Delta_BB\Delta_B$ are small for some nonsingular diagonal matrices $\Delta_A$ and $\Delta_B$.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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