矩阵张量的判定及其Schur补研究

本书特色

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本书专门研究具有广泛应用背景的H-矩阵（张量）的数值判定方法及其应用。全书共分五章，内容包括H矩阵（张量）的基本性质与预备知识，H-矩阵的直接判定方法及迭代判别算法、几类特殊H-矩阵的Schur补对角占优度及特征值分布区域、H-张量的直接判定方法及迭代判别算法、偶次齐次多项式正定性的判定算法及总结和展望。本书的研究将对矩阵（张量）以上领域中出现的具有重要应用背景问题的解决有着积极的意义。

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作者简介

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王峰，男，博士，贵州民族大学理学院副教授，主要从事矩阵（张量）分析与计算的教学和科研工作，研究内容涉及大规模特殊矩阵的分析与计算、大型线性方程组求解、矩阵求逆、矩阵方程、矩阵特征值计算与数值优化、预处理技术、线性互补问题、数值代数、特殊张量的性质和特征值求解等领域。

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目录

目 录第1章 概 述······························································································ 1§1.1 引 言·································································································· 2目 录
第1章 概 述······························································································ 1
§1.1 引 言·································································································· 2
§1.2 研究工作······························································································· 5
第2章 H-矩阵的几种判定法·········································································· 6
§2.1 定义与性质··························································································· 6
§2.2 H-矩阵的一种构造判别法········································································ 9
§2.3 H-矩阵的实用新判据············································································ 14
§2.4 H-矩阵的迭代判别算法········································································· 19
第3章 几类特殊的H-矩阵Schur补的对角占优度及特征值分布························ 31
§3.1 定义与性质·························································································· 32
§3.2 矩阵Schur补的对角占优度及特征值分布················································ 37
§3.3 Ostrowski矩阵Schur补的对角占优度及特征值分布·································· 45
§3.4 块对角占优矩阵Schur补的对角占优度及特征值分布································ 57
第4章 张量的判定及其应用········································································· 74
§4.1 ?? 张量的性质·················································································· 76
§4.2 ?? 张量的直接判定方法····································································· 81
§4.3 ?? 张量的迭代判别算法···································································· 123
§4.4 张量正定的充分条件··········································································· 133
§4.5 张量正定性的判定算法········································································ 134
第5章 总结和展望···················································································· 136
§5.1 总 结······························································································· 136
§5.2 展 望······························································································· 136
参考文献···································································································· 138信息

封面

书名:矩阵张量的判定及其Schur补研究

作者:王峰

页数:149

定价:¥42.0

出版社:西南交通大学出版社

出版日期:2016-06-01

ISBN:9787564347079

PDF电子书大小:61MB 高清扫描完整版