A New Real Structure-preserving Quaternion QR Algorithm
| Autor: | Jia, Zhigang, Wei, Musheng, Zhao, Meixiang, Chen, Yong |
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| Rok vydání: | 2017 |
| Předmět: | |
| Zdroj: | Journal of Computationaland Applied Mathematics 2018 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.cam.2018.04.019 |
| Popis: | 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. Comment: 35 pages, 10 figures |
| Databáze: | arXiv |
| Externí odkaz: |
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