In this paper, we introduce a new subclass of $ H $-matrices called $ {SDD_k} $ matrices, which contains $ {SDD} $ matrices and $ {SDD_1} $ matrices as special cases, and present some properties of $ {SDD_k} $ matrices. Based on these properties, we also provide new infinity norm bounds for the inverse of $ {SDD} $ matrices and $ {SDD_k} $ matrices. It is proved that these new bounds are better than some existing results in some cases. Numerical examples demonstrate the effectiveness of the obtained results.
Citation: Xiaodong Wang, Feng Wang. Infinity norm upper bounds for the inverse of $ {SDD_k} $ matrices[J]. AIMS Mathematics, 2023, 8(10): 24999-25016. doi: 10.3934/math.20231276
In this paper, we introduce a new subclass of $ H $-matrices called $ {SDD_k} $ matrices, which contains $ {SDD} $ matrices and $ {SDD_1} $ matrices as special cases, and present some properties of $ {SDD_k} $ matrices. Based on these properties, we also provide new infinity norm bounds for the inverse of $ {SDD} $ matrices and $ {SDD_k} $ matrices. It is proved that these new bounds are better than some existing results in some cases. Numerical examples demonstrate the effectiveness of the obtained results.
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Xiaodong Wang, Feng Wang. Infinity norm upper bounds for the inverse of $ {SDD_k} $ matrices[J]. AIMS Mathematics, 2023, 8(10): 24999-25016. doi: 10.3934/math.20231276
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