A structure-preserving Jacobi algorithm for quaternion Hermitian eigenvalue problems |
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Authors: | Ru-Ru Ma Zhi-Gang Jia Zheng-Jian Bai |
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Affiliation: | 1. School of Mathematical Sciences, Xiamen University, Xiamen 361005, PR China;2. School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou 221116, PR China |
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Abstract: | A new real structure-preserving Jacobi algorithm is proposed for solving the eigenvalue problem of quaternion Hermitian matrix. By employing the generalized JRS-symplectic Jacobi rotations, the new quaternion Jacobi algorithm can preserve the symmetry and JRS-symmetry of the real counterpart of quaternion Hermitian matrix. Moreover, the proposed algorithm only includes real operations without dimension-expanding and is generally superior to the state-of-the-art algorithm. Numerical experiments are reported to indicate its efficiency and accuracy. |
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Keywords: | Real counterpart Quaternion Hermitian eigenvalue problem Jacobi rotation Structure-preserving algorithm |
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