Fast Givens transformation for quaternion valued matrices applied to Hessenberg reductions (Q2388702)

Two techniques of applying the fast Givens transform to matrices with quaternion valued entries are given. The first is from what is known for the real case. It is shown, that in contrast to the standard opinion it is also possible to store the essential information in only one parameter. The second technique involves four matrices and in each step the authors select that matrix which has the smaller condition number. It is shown that this technique results in a smaller condition number in comparison with the standard technique with only two matrices. The disadvantage of the use of Givens transformation for complex or quaternion valued matrices is pointed out. It is mentioned that fast Givens transformation in the quaternion case needs sixteen times as many flops as the fast Givens transformation applied to real matrices.