Nekrasov张量及其判定

发布时间：2017-12-27 19:25

  本文关键词：Nekrasov张量及其判定　出处：《湘潭大学》2016年硕士论文　论文类型：学位论文

  更多相关文章： 广义Nekrasov张量 正定性 偶数阶超对称实张量

【摘要】：肌矩阵和Nekrasov矩阵都是矩阵理论中极其重要的特殊矩阵类,在数值代数和控制理论等方面具有广泛的应用.最近,H-矩阵已经被扩展到张量的情形,即H-张量.本文将Nekrasov矩阵的形式推到Nekrasov张量,并获得了广义Nekrasov张量与非奇异H-张量等价的关系,进一步给出了Nekrasov张量的一些实用判定.第一章介绍了张量的应用背景和研究现状,给出本文相关的符号说明及定义等.第二章给出了N-张量的定义,证明了N-张量的Hadamard积仍是N-张量,N-张量的主子张量仍是N-张量等性质.第三章探讨了N-张量、广义N-张量与非奇异H-张量之间的关系,得出严格对角占优张量是N-张量,N-张量是非奇异H-张量,以及广义N-张量与非奇异咒-张量等价等结论,进而得出若对角元为正的偶数阶实对称张量A为广义N-张量,则A正定.第四章通过分析张量的元素特征,构造正对角矩阵因子,利用不等式的放缩,给出广义N-张量的直接判别法和迭代判别法,并用数值实例说明判定结果的有效性.
[Abstract]:Muscle and Nekrasov matrices are special matrices is extremely important in the matrix theory, has been widely used in numerical algebra, control theory and so on. Recently, the H- matrix has been extended to tensor case, namely the H- tensor. The Nekrasov matrix form to Nekrasov, and the relationship between the generalized Nekrasov non singular tensor and H- tensor equivalent, further given some practical Nekrasov tensor. The first chapter introduces the application background and research status of the tensor, this paper gives such symbols and definitions. The second chapter gives the definition of the N- tensor, tensor product Hadamard proved that N- is still N- tensor and N- tensor the master is still the N- tensor. Tensor, the third chapter discusses the relationship between N- and generalized N- tensor tensor and nonsingular H- tensor, the tensor is strictly diagonally dominant N- tensor and N- tensor is non singular H- Tensor, and the generalized N- tensor and non singular tensor equivalence incantation conclusion, then if the diagonal elements are even order positive real symmetric tensor A is a generalized N- tensor, A positive definite. In the fourth chapter, through the analysis of characteristics of tensor elements, positive diagonal matrix structure factor, using inequality scaling, generalized N- tensor the direct discriminant method and iterative discriminant validity and numerical examples results.
【学位授予单位】：湘潭大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O183.2
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本文编号：1342884