H-矩阵(张量)的判定及其Schur补研究 本书特色

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。

H-矩阵(张量)的判定及其Schur补研究 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

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自然科学 数学 代数数论组合理论

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