A fast structure-preserving method for computing the singular value decomposition of quaternion matrices

DOI10.1016/j.amc.2014.02.068zbMath1336.65057OpenAlexW2048641947MaRDI QIDQ272393

Musheng Wei, Jianli Zhao, Fengxia Zhang, Ying Li

Publication date: 20 April 2016

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2014.02.068

zbMATH Keywords

structure-preserving algorithmquaternion matrixquaternion singular value decomposition

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Matrices over special rings (quaternions, finite fields, etc.) (15B33)

Related Items (24)

Real structure-preserving algorithms of Householder based transformations for quaternion matrices ⋮ Randomized quaternion QLP decomposition for low-rank approximation ⋮ Accuracy and stability of quaternion Gaussian elimination ⋮ The \(\mathcal{L_C}\)-structure-preserving algorithms of quaternion \(LDL^H\) decomposition and Cholesky decomposition ⋮ On singular value decomposition and generalized inverse of a commutative quaternion matrix and applications ⋮ The forward rounding error analysis of the partial pivoting quaternion LU decomposition ⋮ A new complex structure-preserving method for QSVD ⋮ A complex structure-preserving algorithm for computing the singular value decomposition of a quaternion matrix and its applications ⋮ A real structure-preserving method for the quaternion LU decomposition, revisited ⋮ On condition numbers of quaternion matrix inverse and quaternion linear systems with multiple right-hand sides ⋮ Matrix LSQR algorithm for structured solutions to quaternionic least squares problem ⋮ A new double color image watermarking algorithm based on the SVD and Arnold scrambling ⋮ Special least squares solutions of the quaternion matrix equation \(A X = B\) with applications ⋮ Low Rank Pure Quaternion Approximation for Pure Quaternion Matrices ⋮ A structure-preserving one-sided Jacobi method for computing the SVD of a quaternion matrix ⋮ The equivalence canonical form of five quaternion matrices with applications to imaging and Sylvester-type equations ⋮ Lanczos method for large-scale quaternion singular value decomposition ⋮ On the power method for quaternion right eigenvalue problem ⋮ 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 ⋮ Arnoldi method for large quaternion right eigenvalue problem ⋮ Fixed points results in algebras of split quaternion and octonion ⋮ 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

• Quaternion

Cites Work

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• Block preconditioning of real-valued iterative algorithms for complex linear systems
• Quaternionic Representations of Compact Groups
• Hermitian and Skew-Hermitian Splitting Methods for Non-Hermitian Positive Definite Linear Systems
• The quaternionic determinant
• Principle of General Q Covariance
• Hamilton and Jacobi come full circle: Jacobi algorithms for structured Hamiltonian eigenproblems
• Quaternions and matrices of quaternions

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