A structure-preserving Jacobi algorithm for quaternion Hermitian eigenvalue problems

作者：Ma, Ru-Ru; Jia, Zhi-Gang^*; Bai, Zheng-Jian

来源：Computers & Mathematics with Applications, 2018, 75(3): 809-820.

DOI：10.1016/j.camwa.2017.10.009

• Real counterpart
• Quaternion Hermitian eigenvalue problem
• Jacobi rotation
• Structure-preserving algorithm

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.

• 出版日期2018-2-1
• 单位厦门大学