A New Real Structure-preserving Quaternion QR Algorithm
Abstract
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 forms 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.
Cite
@article{arxiv.1708.02430,
title = {A New Real Structure-preserving Quaternion QR Algorithm},
author = {Zhigang Jia and Musheng Wei and Meixiang Zhao and Yong Chen},
journal= {arXiv preprint arXiv:1708.02430},
year = {2020}
}
Comments
35 pages, 10 figures