%0 Journal Article %1 citeulike:71355 %A Mackey, Niloufer %D 1995 %J SIAM Journal on Matrix Analysis and Applications %K eigenvalue hamilton jacobi problem %N 2 %P 421--435 %T Hamilton and Jacobi Meet Again: Quaternions and the Eigenvalue Problem %U http://citeseer.ist.psu.edu/mackey93hamilton.html %V 16 %X . The algebra isomorphism between M 4 (R) and HØmega\Gamma , where H is the algebra of quaternions, has unexpected computational payoff: it helps construct an orthogonal similarity that 2 \Theta 2 block-diagonalizes a 4 \Theta 4 symmetric matrix. Replacing plane rotations with these more powerful 4 \Theta 4 rotations leads to a quaternion-Jacobi method in which the `weight' of 4 elements (in a 2 \Theta 2 block) is transferred all at once onto the diagonal. Quadratic convergence sets in sooner, ...

@article{citeulike:71355, abstract = {. The algebra isomorphism between M 4 (R) and H\Omega\Gamma , where H is the algebra of quaternions, has unexpected computational payoff: it helps construct an orthogonal similarity that 2 \Theta 2 block-diagonalizes a 4 \Theta 4 symmetric matrix. Replacing plane rotations with these more powerful 4 \Theta 4 rotations leads to a quaternion-Jacobi method in which the `weight' of 4 elements (in a 2 \Theta 2 block) is transferred all at once onto the diagonal. Quadratic convergence sets in sooner, ...}, added-at = {2007-08-18T13:22:24.000+0200}, author = {Mackey, Niloufer}, biburl = {https://www.bibsonomy.org/bibtex/2a057a31d91c97de7fcdad1165f893a51/a_olympia}, citeulike-article-id = {71355}, description = {citeulike}, interhash = {21378837dc98a973c776c3c8014b2365}, intrahash = {a057a31d91c97de7fcdad1165f893a51}, journal = {SIAM Journal on Matrix Analysis and Applications}, keywords = {eigenvalue hamilton jacobi problem}, number = 2, pages = {421--435}, timestamp = {2007-08-18T13:22:58.000+0200}, title = {Hamilton and Jacobi Meet Again: Quaternions and the Eigenvalue Problem}, url = {http://citeseer.ist.psu.edu/mackey93hamilton.html}, volume = 16, year = 1995 }