A new structure-preserving method for quaternion Hermitian eigenvalue problems

Authors:
Zhigang Jia;Musheng Wei;Sitao Ling
Affiliations:
School of Mathematical Sciences, Jiangsu Normal University, Jiangsu, 221116, PR China;College of Mathematics and Science, Shanghai Normal University, Shanghai 200234, PR China;College of Science, China University of Mining and Technology, Jiangsu, 221116, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2013

Citing 5
Cited 0

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Abstract

In this paper we propose a novel structure-preserving algorithm for solving the right eigenvalue problem of quaternion Hermitian matrices. The algorithm is based on the structure-preserving tridiagonalization of the real counterpart for quaternion Hermitian matrices by applying orthogonal JRS-symplectic matrices. The algorithm is numerically stable because we use orthogonal transformations; the algorithm is very efficient, it costs about a quarter arithmetical operations, and a quarter to one-eighth CPU times, comparing with standard general-purpose algorithms. Numerical experiments are provided to demonstrate the efficiency of the structure-preserving algorithm.