Real structure-preserving algorithms of Householder based transformations for quaternion matrices
From MaRDI portal
Publication:277197
DOI10.1016/j.cam.2016.03.031zbMath1386.65120OpenAlexW2318781916MaRDI QIDQ277197
Ying Li, Fengxia Zhang, Musheng Wei, Jianli Zhao
Publication date: 4 May 2016
Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.cam.2016.03.031
Matrices over special rings (quaternions, finite fields, etc.) (15B33) Orthogonalization in numerical linear algebra (65F25)
Related Items
A new real structure-preserving quaternion QR algorithm ⋮ Randomized quaternion QLP decomposition for low-rank approximation ⋮ Randomized Quaternion Singular Value Decomposition for Low-Rank Matrix Approximation ⋮ Accuracy and stability of quaternion Gaussian elimination ⋮ 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 ⋮ Efficient iterative method for generalized Sylvester quaternion tensor equation ⋮ On condition numbers of quaternion matrix inverse and quaternion linear systems with multiple right-hand sides ⋮ Randomized low rank approximation for nonnegative pure quaternion matrices ⋮ Matrix LSQR algorithm for structured solutions to quaternionic least squares problem ⋮ A structure-preserving Jacobi algorithm for quaternion Hermitian eigenvalue problems ⋮ A new double color image watermarking algorithm based on the SVD and Arnold scrambling ⋮ Low Rank Pure Quaternion Approximation for Pure Quaternion Matrices ⋮ A structure-preserving one-sided Jacobi method for computing the SVD of a quaternion matrix ⋮ 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 ⋮ 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 ⋮ On accurate error estimates for the quaternion least squares and weighted least squares problems
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A fast structure-preserving method for computing the singular value decomposition of quaternion matrices
- On preconditioned MHSS iteration methods for complex symmetric linear systems
- Quaternion singular value decomposition based on bidiagonalization to a real or complex matrix using quaternion Householder transformations
- Jacobi method for quaternion matrix singular value decomposition
- A structure-preserving algorithm for the quaternion Cholesky decomposition
- Modified HSS iteration methods for a class of complex symmetric linear systems
- Matrix factorizations for symplectic QR-like methods
- A quaternion QR-algorithm
- A new structure-preserving method for quaternion Hermitian eigenvalue problems
- Singular value decomposition and least squares solutions
- Implementing Linear Algebra Algorithms for Dense Matrices on a Vector Pipeline Machine
- Block preconditioning of real-valued iterative algorithms for complex linear systems
- Hyperbolic householder transformations
- Quaternionic Representations of Compact Groups
- The quaternionic determinant
- Principle of General Q Covariance
- Remarks on the Unitary Triangularization of a Nonsymmetric Matrix
- Unitary Triangularization of a Nonsymmetric Matrix
- Hamilton and Jacobi come full circle: Jacobi algorithms for structured Hamiltonian eigenproblems
- Quaternions and matrices of quaternions
