A fast decomposition of banded symmetric Toeplitz matrices for parallel processing

The eigendecomposition of banded symmetric matrices Is important in regularized signal restoration. In this paper a new fast decomposition algorithm is developed by using FFT and rank-one update. In this way the split of the matrix becomes more direct and the cost of the initial decomposition decreases. The algorithm is especially useful for parallel processing. Two numerical examples are given, which show that the new method can achieve comparable results to the classical methods