engleski

Convergence of the complex cyclic Jacobi methods and applications

We prove global convergence of the complex Jacobi method for a large class of the generalized serial cyclic pivot strategies. We find a constant $\gamma<1$ such that for a given Hermitian matrix $A$ we have $S(A')\leq\gamma*S(A)$, where $A'$ is obtained from $A$ by applying one cycle of the Jacobi method and $S(.)$ stands for the off-norm. The theory of the Jacobi operators is used. The obtained results are applied to the generalized eigenvalue problem.

Jacobi methods ; eigenvalue problem ; generalized eigenvalue problem ; convergence ; pivot strategies

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