Jacobi-like Algorithms for Eigenvalue Decomposition of a Real Normal Matrix Using Real Arithmetic
IPPS '96 Proceedings of the 10th International Parallel Processing Symposium
Structural invariance of spatial Pythagorean hodographs
Computer Aided Geometric Design
An efficient method for computing eigenvalues of a real normal matrix
Journal of Parallel and Distributed Computing
Quaternion involutions and anti-involutions
Computers & Mathematics with Applications
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The algebra isomorphism between $\cal{M}_{4}(\cal{R})$ and $\cal{H} \otimes \cal{H}$, where $\cal{H}$ is the algebra of quaternions, has unexpected computational payoff: it helps construct an orthogonal similarity that $2 \times 2$ block-diagonalizes a $4\times 4$ symmetric matrix. Replacing plane rotations with these more powerful $4 \times 4$ rotations leads to a quaternion-Jacobi method in which the "weight" of four elements (in a $2 \times 2$ block) is transferred all at once onto the diagonal. Quadratic convergence sets in sooner, and the new method requires at least one fewer sweep than plane-Jacobi methods. An analogue of the sorting angle for plane rotations is developed for these $4 \times 4$ rotations.