本文關(guān)鍵詞：Nekrasov張量及其判定　出處：《湘潭大學(xué)》2016年碩士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： 廣義Nekrasov張量 正定性 偶數(shù)階超對(duì)稱實(shí)張量

【摘要】：肌矩陣和Nekrasov矩陣都是矩陣?yán)碚撝袠O其重要的特殊矩陣類,在數(shù)值代數(shù)和控制理論等方面具有廣泛的應(yīng)用.最近,H-矩陣已經(jīng)被擴(kuò)展到張量的情形,即H-張量.本文將Nekrasov矩陣的形式推到Nekrasov張量,并獲得了廣義Nekrasov張量與非奇異H-張量等價(jià)的關(guān)系,進(jìn)一步給出了Nekrasov張量的一些實(shí)用判定.第一章介紹了張量的應(yīng)用背景和研究現(xiàn)狀,給出本文相關(guān)的符號(hào)說(shuō)明及定義等.第二章給出了N-張量的定義,證明了N-張量的Hadamard積仍是N-張量,N-張量的主子張量仍是N-張量等性質(zhì).第三章探討了N-張量、廣義N-張量與非奇異H-張量之間的關(guān)系,得出嚴(yán)格對(duì)角占優(yōu)張量是N-張量,N-張量是非奇異H-張量,以及廣義N-張量與非奇異咒-張量等價(jià)等結(jié)論,進(jìn)而得出若對(duì)角元為正的偶數(shù)階實(shí)對(duì)稱張量A為廣義N-張量,則A正定.第四章通過(guò)分析張量的元素特征,構(gòu)造正對(duì)角矩陣因子,利用不等式的放縮,給出廣義N-張量的直接判別法和迭代判別法,并用數(shù)值實(shí)例說(shuō)明判定結(jié)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.
【學(xué)位授予單位】：湘潭大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2016
【分類號(hào)】：O183.2
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本文編號(hào)：1342884