Second Order Sequential Best Rotation Algorithm with Householder Reduction for Polynomial Matrix Eigenvalue Decomposition

The Second-order Sequential Best Rotation (SBR2) algorithm, used for Eigenvalue Decomposition (EVD) on para-Hermitian polynomial matrices typically encountered in wideband signal processing applications like multichannel Wiener filtering and channel coding, involves a series of delay and rotation operations to achieve diagonalisation. In this paper, we proposed the use of Householder transformations to reduce polynomial matrices to tridiagonal form before zeroing the dominant element with rotation. Similar to performing Householder reduction on conventional matrices, our method enables SBR2 to converge in fewer iterations with smaller order of polynomial matrix factors because more off-diagonal Frobenius-norm (F-norm) could be transferred to the main diagonal at every iteration. A reduction in the number of iterations by 12.35% and 0.1% improvement in reconstruction error is achievable.