A unitary Hessenberg QR-based algorithm via semiseparable matrices

[摘要] In this paper, we present a novel method for solving the unitary Hessenberg eigenvalue problem. In the first phase, an algorithm is designed to transform the unitary matrix into a diagonal-plus-semiseparable form. Then we rely on our earlier adaptation of the QR algorithm to solve the dpss eigenvalue problem in a fast and robust way. Exploiting the structure of the problem enables us to yield a quadratic time using a linear memory space. Nonetheless the algorithm remains robust and converges as fast as the customary QR algorithm. Numerical experiments confirm the effectiveness and the robustness of our approach. (c) 2005 Elsevier B.V. All rights reserved.

[发布日期] 2005-12-15

[关键词] unitary Hessenberg matrices;QR iteration;Eigenvalue computation;semiseparable matrices