On Rayleigh Quotient Iteration for Dual Quaternion Hermitian Eigenvalue Problem

2023/10/31 by Shan‐Qi Duan, Qing‐Wen Wang, Duan, Shan-Qi +3 · 1 citation
Computer Science · #Distributed Control Multi-Agent Systems #FOS: Mathematics #Matrix Theory and Algorithms #Neural Networks Stability and Synchronization #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2310.20290

openalex publication_date 2023/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The application of eigenvalue theory to dual quaternion Hermitian matrices holds significance in the realm of multi-agent formation control. In this paper, we study the Rayleigh quotient iteration (RQI) for solving the right eigenpairs of dual quaternion Hermitian matrices. Combined with dual representation, the RQI algorithm can effectively compute the eigenvalue along with the associated eigenvector of the dual quaternion Hermitian matrices. Furthermore, by utilizing minimal residual property of the Rayleigh Quotient, a convergence analysis of the Rayleigh quotient iteration is derived. Numerical examples are provided to illustrate the high accuracy and low CPU time cost of the proposed Rayleigh quotient iteration compared with the power method for solving the dual quaternion Hermitian eigenvalue problem.

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• The Power Method for Non-Hermitian Dual Quaternion Matrices

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