两类双结构矩阵特征值问题的向后误差

Backward Errors for Two Kinds of Doubly Structured Matrix Eigenvalue Problems

讨论2类双结构矩阵特征值问题的向后误差公式和上下界。这2类结构矩阵分别是反对称正交阵和反对称反Hamilton阵。使用的主要技术是基于正交辛相似变换。所得结果可看作Tisseur提出的2个待解决问题的回答。

We present formulae and bounds for structured backward errors for two kinds of real doubly structured matrix eigenvalue problems. The structured matrices considered in this paper are skew-symmetric orthogonal and skew symmetric skew-Hamiltonian matrices, respectively. The technique we used is mainly based on orthogonal symplectic similarity transformations. The results obtained in this paper can be viewed as answers to two open questions raised by Tisseur.