Fast Givens Rotation Approach to Second Order Sequential Best Rotation Algorithms

The second order sequential best rotation (SBR2) algorithm is a popular algorithm to decompose a parahermitian matrix into approximate polynomial eigenvalues and eigenvectors. The work horse behind SBR2 is a Givens rotation interspersed by delay operations. In this paper, we investigate and analyse the application of a fast Givens rotation in order to reduce the computation complexity of SBR2. The proposed algorithm inherits the SBR2’s proven convergence to a diagonalised and spectrally majorised solution for the polynomial eigenvalues. We provide some analysis and examples for the execution speed of this fast Givens-based SBR2 compared to a standard SBR2 implementation.