K层Nekrasov矩阵与广义严格对角占优矩阵的关系研究  

Relationship of K Layer Nekrasov Matrix and Generalized Strictly Diagonally Dominant Matrix

作　　者：尹锋[1] 刘仲博[1] 

机构地区：[1]宁夏职业技术学院电子与信息技术系,宁夏银川750021

出　　处：《科技通报》2013年第9期11-14,共4页Bulletin of Science and Technology

基　　金：宁夏高等学校科学技术研究项目资助(NGY2012124)

摘　　要：K层Nekrasov矩阵的推广矩阵中,K层弱Nekrasov矩阵与广义严格对角占优矩阵存在迭代矩阵和不等式估计等性质,本文针对这几类矩阵与广义严格对角占优矩阵之间的置换关系进行了定义和证明,并根据广义Nekrasov矩阵与弱Nekrasov矩阵的置换不变性,推论出非奇异矩阵的充要条件,将广义K层Nekrasov矩阵和K层弱Nekrasov矩阵的对角阵的奇异性进行了充要性的推论和证明。进而通过构造特殊矩阵和特殊向量改进了广义Nekrasov矩阵研究中的不足。Promotion matrix of the the K layer Nekrasov matrix, the K layer weak Nekrasov matrix and generalized strictly diagonally dominant matrix exists iterative matrix and inequality estimates nature, for these types of matrices and generalized strictly diagonally dominant matrices replacement relations carried out to define and prove, and invariance under the generalized of Nekrasov matrices with weak Nekrasov matrix replacement, to infer the necessary and sufficient conditions for non-singular matrix, the generalized K layer Nekrasov matrix K layer weak Nekrasov matrix diagonal matrix singularitythe sufficient and necessary inference and proof. Further improved by constructing a special matrix and special vector inadequate study generalized Nekrasov matrix.

关 键 词：K层Nekrasov矩阵 弱Nekrasov矩阵 广义严格对角占优矩阵 不等式估计 

分 类 号：O151.21[理学—数学]