A New Complex Structure-Preserving Method for QSVD

Yu, Cui-E; Liu, Xin; Zhang, Yang

doi:10.1007/s10915-024-02496-3

J Sci Comput

2024

DOI: 10.1007/s10915-024-02496-3

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A New Complex Structure-Preserving Method for QSVD

Cui-E Yu,

Xin Liu,

Yang Zhang

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2024

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On Rayleigh Quotient Iteration for the Dual Quaternion Hermitian Eigenvalue Problem

Duan,

Wang,

Duan

2024

Mathematics

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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 use of 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 the 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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On Rayleigh Quotient Iteration for the Dual Quaternion Hermitian Eigenvalue Problem

Duan,

Wang,

Duan

2024

Mathematics

View full text Add to dashboard Cite

show abstract

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A New Complex Structure-Preserving Method for QSVD

Cited by 1 publication

References 14 publications

On Rayleigh Quotient Iteration for the Dual Quaternion Hermitian Eigenvalue Problem

On Rayleigh Quotient Iteration for the Dual Quaternion Hermitian Eigenvalue Problem

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