《張量特徵值的定位及其套用研究》是依託雲南大學，由李耀堂擔任負責人的國家自然科學基金資助地區科學基金項目。
基本介紹
- 中文名：張量特徵值的定位及其套用研究
- 依託單位：雲南大學
- 項目負責人：李耀堂
- 項目類別：地區科學基金項目
項目簡介,科研成果,
項目簡介
本項目擬套用理論研究與數值模擬相結合的方法，研協漿霉究張量特徵值定位（即分布、估計和計算）的相關微酷擊理論和套用問題。首先對高階張量的各類特徵值（如H-特徵值、Z-特徵值、N-特徵值、E-特徵值、D-特徵值、M-特徵值和B-特徵值等）以及它們之間的聯繫與區別進行深入系統研究，並在此基礎上，研究一般高階張量的幾類重要特徵值的分布問題，以期得到這些特徵值的儘可能精確的包含區域和數值特徵。然後將這些結果套用於幾類重要的特殊張量（如非陵享旬葛負張量、超對稱張量、M-張量和H-張量等）的特徵值的滲背戲分布、估計和計算研究，在完善理論的基礎上提供這些張量特徵值的一些實用逼近算法。最後套用這些性質和槳陵兵算法研究高階偶次齊次多元多項式正定性的判定問題，期望得到偶次齊次多元多項式正定性的一些新的適用判定算法。 本項目預期在國內外專業刊物上發表10篇以上較高水平的研究論文，其中SCI摘引刊物上發表6篇以上。
科研成果
序故舟號 | 標題 | 類型 | 作者 |
|---|---|---|---|
1 | Gersgorin-type and Brauer-type eigenvalue localization sets of stochastic matrices | 期刊論文 | Li, Chaoqian，蘭甩晚遙Liu, Qingbing，Li, Yaotang(*) |
2 | A New Upper Bound on the Infinity Norm of the Inverse of Nekrasov Matrices | 期刊論文 | Gao, Lei，Li, Chaoqian，Li, Yaotang(*) |
3 | Subdirect sums of Nekrasov matrices | 期刊論文 | Li, Chaoqian，Liu, Qilong，Gao, Lei，Li, Yaotang(*) |
4 | A new Brauer-type eigenvalue localization set for tensors | 期刊論文 | Li, Chaoqian，Zhou, Jianjun，Li, Yaotang(*) |
5 | An eigenvalue localization set for tensors with applications to determine the positive (semi-)definiteness of tensors | 期刊論文 | Li, Chaoqian，Li, Yaotang(*) |
6 | Some new preconditioned generalized AOR methods for generalized least-squares problems | 期刊論文 | Zhao, Jianxing，Li, Chaoqian，Wang, Feng，Li, Yaotang(*) |
7 | Camera self-calibration based on circular points with two planar mirrors using silhouettes | 期刊論文 | Zhao, Yue，Zhang, Xiaofen，Wang, Yalin，Xu, Limin |
8 | Subdirect sums of Nekrasov matrices | 期刊論文 | Li, Chaoqian，Liu, Qilong，Gao, Lei，Li, Yaotang(*) |
9 | Calibration of a paracatadioptric camera by projection imaging of a single sphere | 期刊論文 | Li, Yuanzhen，Zhao, Yue |
10 | Bounds for the Z-eigenpair of general nonnegative tensors | 期刊論文 | Liu, Qilong，Li, Yaotang(*) |
11 | A linear approach for determining camera intrinsic parameters using tangent circles | 期刊論文 | Chen, Xu，Zhao, Yue |
12 | SIMPLIFICATIONS OF THE OSTROWSKI UPPER BOUNDS FOR THE SPECTRAL RADIUS OF NONNEGATIVE MATRICES | 期刊論文 | Li, Chaoqian，Hu, Baohua，Li, Yaotang(*) |
13 | Minimal Gersgorin tensor eigenvalue inclusion set and its approximation | 期刊論文 | Li, Chaoqian，Zhang, Chengyi，Li, Yaotang(*) |
14 | An S-type eigenvalue localization set for tensors | 期刊論文 | Li, Chaoqian，Jiao, Aiquan，Li, Yaotang(*) |
15 | p-Norm SDD tensors and eigenvalue localization | 期刊論文 | Liu, Qilong，Li, Yaotang(*) |
16 | BOUNDS FOR THE SPECTRAL RADIUS OF NONNEGATIVE TENSORS | 期刊論文 | Li, Chaoqian(*)，Wang, Yaqiang(*)，Yi, Jieyi(*)，Li, Yaotang(*) |
17 | Note on error bounds for linear complementarity problems for B-matrices | 期刊論文 | Li, Chaoqian，Li, Yaotang(*) |
18 | An eigenvalue localization set for tensors with applications to determine the positive (semi-)definiteness of tensors | 期刊論文 | Li, Chaoqian，Li, Yaotang(*) |
19 | Improvements on the infinity norm bound for the inverse of Nekrasov matrices | 期刊論文 | Li, Chaoqian(*)，Pei, Hui，Gao, Aning，Li, Yaotang |
20 | Minimal Gersgorin tensor eigenvalue inclusion set and its approximation | 期刊論文 | Li, Chaoqian，Zhang, Chengyi，Li, Yaotang(*) |
21 | Person Re-Identification by Dual-Regularized KISS Metric Learning | 期刊論文 | Tao, Dapeng(*)，Guo, Yanan(*)，Song, Mingli(*)，Li, Yaotang(*)，Yu, Zhengtao(*)，Tang, Yuan Yan(*) |
22 | The projected circle centres and polar line for camera self-calibration | 期刊論文 | Chen, Xu，Zhao, Yue |
23 | MB-tensors and MB0-tensors | 期刊論文 | Li, Chaoqian，Qi, Liqun，Li, Yaotang(*) |
24 | Improvements on the infinity norm bound for the inverse of Nekrasov matrices | 期刊論文 | Li, Chaoqian(*)，Pei, Hui，Gao, Aning，Li, Yaotang |
25 | BOUNDS FOR THE SPECTRAL RADIUS OF NONNEGATIVE TENSORS | 期刊論文 | Li, Chaoqian(*)，Wang, Yaqiang(*)，Yi, Jieyi(*)，Li, Yaotang(*) |
26 | Some new bounds for the minimum eigenvalue of the Hadamard product of an M-matrix and an inverse M-matrix | 期刊論文 | Li, Yao-tang(*)，Wang, Feng，Li, Chao-qian，Zhao, Jian-xing |
27 | A new Brauer-type eigenvalue localization set for tensors | 期刊論文 | Li, Chaoqian，Zhou, Jianjun，Li, Yaotang(*) |
28 | Subdirect sums of weakly chained diagonally dominant matrices | 期刊論文 | Li, Chaoqian，Ma, Ruidan，Liu, Qilong，Li, Yaotang |
29 | Relationships between Brauer-type eigenvalue inclusion sets and a Brualdi-type eigenvalue inclusion set for tensors | 期刊論文 | Li, Chaoqian，Li, Yaotang(*) |
30 | A new eigenvalue inclusion set for tensors and its applications | 期刊論文 | Li, Chaoqian，Chen, Zhen，Li, Yaotang(*) |
31 | New error bounds for linear complementarity problems of Nekrasov matrices and B-Nekrasov matrices | 期刊論文 | Li, Chaoqian，Dai, Pingfan，Li, Yaotang(*) |
32 | Gersgorin-type and Brauer-type eigenvalue localization sets of stochastic matrices | 期刊論文 | Li, Chaoqian，Liu, Qingbing，Li, Yaotang(*) |
33 | A new Brauer-type eigenvalue localization set for tensors | 期刊論文 | Li, Chaoqian，Zhou, Jianjun，Li, Yaotang(*) |
34 | Note on error bounds for linear complementarity problems for B-matrices | 期刊論文 | Li, Chaoqian，Li, Yaotang(*) |
35 | Method to solve intrinsic geometric parameters of a paracatadioptric camera using 3D lines | 期刊論文 | Zhao, Yue，Gu, Wanjia |
36 | An eigenvalue localization set for tensors with applications to determine the positive (semi-)definiteness of tensors | 期刊論文 | Li, Chaoqian，Li, Yaotang(*) |
