α-Chain Diagonally Dominant Matrix and Criterion for Nonsingular H -Matrix

doi:10.3696/j.issn.1672-6952.2010.02.021

Journal of Liaoning Petrochemical University ›› 2010, Vol. 30 ›› Issue (2): 74-77.DOI: 10.3696/j.issn.1672-6952.2010.02.021

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α-Chain Diagonally Dominant Matrix and Criterion for Nonsingular H -Matrix

WANG Ming-gang， SONG Dai-cai*, MIAO Chen

School of Science, Liaoning Shihua University, Fushun Liaoning 113001, P.R.China

Received:2009-04-10 Published:2010-06-25 Online:2017-07-05

α-链对角占优矩阵与非奇异H -矩阵的判别

王明刚,宋岱才* ,苗晨

辽宁石油化工大学理学院,辽宁抚顺113001

作者简介:王明刚(1985-),男,辽宁沈阳市,在读硕士。
基金资助:
辽宁省教育厅高校科研项目(2004F100);辽宁石油化工大学重点学科建设资助项目(J200874)。

Abstract

Abstract:

Let A=( a_ij)∈Cⁿ^×n, if there exists α∈ (0,1) which can make|a_ii|≥R^α_i(A)S^1-^α_i(A) be right for i∈N={1,2,…,n}, then A is called a chain diagonally dominant matrix. the concept was extended to generalized α-chain diagonally dominant matrix，and the concept generalized α-chain diagonally dominant matrix was applied to obtain some new criteria condition for a matrix to be a nonsingular H-matrix. The results obtained improve the known corresponding results．Finally, a numerical example was given for illustrating advantage of results．

Key words: α-Chain diagonally dominant matrix , Irreducible matrix , Nonsingular H-matrix

摘要： 设A=(a_ij)∈C^n×n ,若存在α∈(0,1),使∀i∈N ={1,2,…,n},|aii|≥R ^α_i (A)S ^1-α_i (A),则称A 为α-链对角占优矩阵。首先推广α-链对角占优矩阵的概念到广义α-链对角占优矩阵;利用这一概念得到了判别非奇异H -矩阵的几个判定方法,改进和推广了已有的结论。最后用数值例子说明了所给结果的优越性。

关键词: &alpha, -链对角占优矩阵 , 不可约矩阵 , 非奇异H -矩阵

WANG Ming-gang， SONG Dai-cai, MIAO Chen. α-Chain Diagonally Dominant Matrix and Criterion for Nonsingular H -Matrix[J]. Journal of Liaoning Petrochemical University, 2010, 30(2): 74-77.

王明刚,宋岱才,苗晨. α-链对角占优矩阵与非奇异H -矩阵的判别[J]. 辽宁石油化工大学学报, 2010, 30(2): 74-77.

α-Chain Diagonally Dominant Matrix and Criterion for Nonsingular H -Matrix

α-链对角占优矩阵与非奇异H -矩阵的判别

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