Multiple shift second order sequential best rotation algorithm for polynomial matrix EVD

In this paper, we present an improved version of the second order sequential best rotation algorithm (SBR2) for polynomial matrix eigenvalue decomposition of para-Hermitian matrices. The improved algorithm is entitled multiple shift SBR2 (MS-SBR2) which is developed based on the original SBR2 algorithm. It can achieve faster convergence than the original SBR2 algorithm by means of transferring more off-diagonal energy onto the diagonal at each iteration. Its convergence is proved and also demonstrated by means of a numerical example. Furthermore, simulation results are included to compare its convergence characteristics and computational complexity with the original SBR2, sequential matrix diagonalization (SMD) and multiple shift maximum element SMD algorithms.