A fast wavelet block Jacobi method

In this paper, we develop a fast block Jacobi method for linear systems based on discrete wavelet transform (DWT). Traditional wavelet-based methods for linear systems do not fully utilize the sparsity and the multi-level block structure of the transformed matrix after DWT. For the sake of numerical efficiency, we truncate the transformed matrix to be a sparse matrix by letting the small values be zero. To combine the advantages of the direct method and the iterative method, we solve the sub-systems appropriately based on the multi-level block structure of the transformed matrix after DWT. Numerical examples show that the proposed method is very numerically effective.