A Wilkinson-like multishift QR algorithm for symmetric eigenvalue problems and its global convergence

作者：Aishima Kensuke^*; Matsuo Takayasu; Murota Kazuo; Sugihara Masaaki

来源：Journal of Computational and Applied Mathematics, 2012, 236(15): 3556-3560.

DOI：10.1016/j.cam.2011.04.012

• Numerical linear algebra
• Eigenvalue
• Symmetric tridiagonal matrix

In 1989, Bai and Demmel proposed the multishift QR algorithm for eigenvalue problems. Although the global convergence property of the algorithm (i.e., the convergence from any initial matrix) still remains an open question for general nonsymmetric matrices, in 1992 Jiang focused on symmetric tridiagonal case and gave a global convergence proof for the generalized Rayleigh quotient shifts. In this paper, we propose Wilkinson-like shifts, which reduce to the standard Wilkinson shift in the single shift case, and show a global convergence theorem.

• 出版日期2012-9