A Structure-Preserving One-Sided Jacobi Method for Computing the SVD of a Quaternion Matrix
For researchers working with quaternion matrices in areas like signal processing or computer graphics, this method offers a more efficient SVD computation by preserving structure, though it is an incremental improvement over existing Jacobi methods.
The paper presents a structure-preserving one-sided Jacobi method for computing the SVD of quaternion matrices, achieving quadratic convergence under mild conditions, with numerical tests demonstrating efficiency.
In this paper, we provide a structure-preserving one-sided cyclic Jacobi method for computing the singular value decomposition of a quaternion matrix. In this method, the columns of the quaternion matrix are orthogonalized in pairs by using a sequence of orthogonal JRS-symplectic Jacobi matrices to its real counterpart. The quadratic convergence is also established under some mild conditions. Numerical tests are reported to illustrate the efficiency of the proposed method.