Bulge Exchanges in Gz Algorithms for the Standard and Generalized Eigenvalue Problems
نویسنده
چکیده
One of the most important methods for solving the generalized eigenvalue problem Av = λBv is the QZ algorithm, which is a member of the larger class of GZ algorithms. These are normally implemented implicitly as bulge chasing algorithms. We show how to effect rational implicit GZ iterations by chasing bulges in both directions and passing them through each other. Application of this procedure to the standard eigenvalue problem Av = λv results in a simplified method for effecting rational GR iterations. Numerical experience suggests that the method works well in practice if the degrees of the bulges are no bigger than two. Further testing will be needed before we know for sure.
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