A fast wavelet block Jacobi method |
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Authors: | Dongsheng Cheng Chunyuan Lu Taishan Zeng |
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Affiliation: | 1. Guangdong Province Key Laboratory of Computational Science, Sun Yat-Sen University, Guangzhou 510275, PR China;2. College of Medical Information Engineering, Guangdong Pharmaceutical University, Guangzhou 510006, PR China;3. School of Mathematical Sciences, South China Normal University, Guangzhou 510631, PR China |
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Abstract: | 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. |
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