Abstract
In this paper we prove the global convergence of the complex Jacobi method for Hermitian matrices for a large class of generalized serial pivot strategies. For a given Hermitian matrix A of order n we find a constant depending on n, such that , where is obtained from A by applying one or more cycles of the Jacobi method and stands for the off-diagonal norm. Using the theory of complex Jacobi operators, the result is generalized so it can be used for proving convergence of more general Jacobi-type processes. In particular, we use it to prove the global convergence of Cholesky–Jacobi method for solving the positive definite generalized eigenvalue problem.
Acknowledgements
The authors are thankful to the anonymous reviewers for their suggestions and comments.
Disclosure statement
No potential conflict of interest was reported by the authors.