Analysis of the structured perturbation for the BSCCB linear system

In this paper, based on block style spectral decomposition of the block skew circulant with circulant blocks (BSCCB) matrix, the structure perturbation is discussed, which includes the condition number and relative error of the BSCCB linear system. Then the optimal backward perturbation bound of the BSCCB linear system is analyzed. Simultaneously, the algorithm for the optimal backward perturbation bound is presented. At the end of the paper, a numerical example is provided to verify the effectiveness of the algorithm.