A real structure-preserving method for the quaternion LU decomposition, revisited

DOI10.1007/s10092-017-0241-4zbMath1382.65073OpenAlexW2766897841MaRDI QIDQ1697294

Musheng Wei, Ying Li, Jianli Zhao, Fengxia Zhang

Publication date: 15 February 2018

Published in: Calcolo (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10092-017-0241-4

zbMATH Keywords

algorithmreal representationnumerical experimentpartial pivotingquaternion matrixLU decompositionstructure-preserving method

Mathematics Subject Classification ID

Matrices over special rings (quaternions, finite fields, etc.) (15B33) Direct numerical methods for linear systems and matrix inversion (65F05)

Related Items (14)

Randomized quaternion QLP decomposition for low-rank approximation ⋮ Randomized Quaternion Singular Value Decomposition for Low-Rank Matrix Approximation ⋮ Computing partial quaternion eigenpairs with quaternion shift ⋮ Quaternion matrix decomposition and its theoretical implications ⋮ Accuracy and stability of quaternion Gaussian elimination ⋮ The \(\mathcal{L_C}\)-structure-preserving algorithms of quaternion \(LDL^H\) decomposition and Cholesky decomposition ⋮ The forward rounding error analysis of the partial pivoting quaternion LU decomposition ⋮ A complex structure-preserving algorithm for computing the singular value decomposition of a quaternion matrix and its applications ⋮ Structure Preserving Quaternion Biconjugate Gradient Method ⋮ On condition numbers of quaternion matrix inverse and quaternion linear systems with multiple right-hand sides ⋮ An algorithm based on QSVD for the quaternion equality constrained least squares problem ⋮ A complex structure-preserving algorithm for split quaternion matrix \textit{LDU} decomposition In split quaternion mechanics ⋮ A complex structure-preserving algorithm for the full rank decomposition of quaternion matrices and its applications ⋮ A real structure-preserving algorithm based on the quaternion QR decomposition for the quaternion equality constrained least squares problem

Uses Software

• Matlab
• Quaternion

Cites Work

• Unnamed Item
• A fast structure-preserving method for computing the singular value decomposition of quaternion matrices
• Real structure-preserving algorithms of Householder based transformations for quaternion matrices
• A structure-preserving method for the quaternion LU decomposition in quaternionic quantum theory
• Jacobi method for quaternion matrix singular value decomposition
• A structure-preserving algorithm for the quaternion Cholesky decomposition

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