A new structure-preserving method for quaternion Hermitian eigenvalue problems

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:239

Article

Jia, Zhigang²  Wei, Musheng¹  Ling, Sitao³ 

[1] Shanghai Normal Univ, Coll Math & Sci, Shanghai 200234, Peoples R China

[2] Jiangsu Normal Univ, Sch Math Sci, Jiangsu 221116, Peoples R China

[3] China Univ Min & Technol, Coll Sci, Jiangsu 221116, Peoples R China

关键词: Quaternion Hermitian operator;    Quaternionic right eigenvalue problem;    Structure-preserving algorithm;   

DOI  :  10.1016/j.cam.2012.09.018

来源: Elsevier

【 摘 要 】

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. (C) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

Free