engleski

Globally convergent Jacobi methods for positive definite matrix pairs

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 $\Delta_B$.

Generalized eigenvalue problem ; Jacobi method ; Global convergence

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