A new real structure-preserving quaternion QR algorithm

作者：Jia, Zhigang^*; Wei, Musheng; Zhao, Mei-Xiang; Chen, Yong

来源：Journal of Computational and Applied Mathematics, 2018, 343: 26-48.

DOI：10.1016/j.cam.2018.04.019

• Structured matrices
• Structure-preserving method
• Quaternion QR algorithm
• Quaternion eigenvalue problem

New real structure-preserving decompositions are introduced to develop fast and robust algorithms for the (right) eigenproblem of general quaternion matrices. Under the orthogonally JRS-symplectic transformations, the Francis JRS-QR step and the JRS-QR algorithm are firstly proposed for JRS-symmetric matrices and then applied to calculate the Schur form of quaternion matrices. A novel quaternion Givens matrix is defined and utilized to compute the QR factorization of quaternion Hessenberg matrices. An implicit double shift quaternion QR algorithm is presented with a technique for automatically choosing shifts and within real operations. Numerical experiments are provided to demonstrate the efficiency and accuracy of newly proposed algorithms.

• 出版日期2018-12-1
• 单位上海师范大学; 中国矿业大学（北京）