A Structure-Preserving One-Sided Jacobi Method for Computing the SVD of a Quaternion Matrix

2018/11/21 by Ru‐Ru Ma, Ma, Ru-Ru, Zheng‐Jian Bai +1
Computer Science · Materials Science · Physics and Astronomy · #Electromagnetic Scattering and Analysis #FOS: Mathematics #Liquid Crystal Research Advancements #Matrix Theory and Algorithms #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1811.08671

openalex publication_date 2018/11/21 · openalex created_date 2018/11/29 · openalex updated_date 2026/07/28

Abstract

In this paper, we provide a structure-preserving one-sided cyclic Jacobi method for computing the singular value decomposition of a quaternion matrix. In this method, the columns of the quaternion matrix are orthogonalized in pairs by using a sequence of orthogonal JRS-symplectic Jacobi matrices to its real counterpart. The quadratic convergence is also established under some mild conditions. Numerical tests are reported to illustrate the efficiency of the proposed method.

Citations

• Quaternions and matrices of quaternions

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