多元统计分析中一类矩阵迹函数最小化问题的有效算法

研究来源于多元统计分析中的一类矩阵迹函数最小化问题$\min c+ tr(AX)+\sum\limits_{j=1}^{m}tr(B_j X C_jX^{T}),\ \ {\rm s. t.} \ X^TX=I_p,$其中$c$为常数, $A\in R^{p\times n}\ (n\geq p)$, $B_j\in R^{n\times n}, C_j\in R^{p\times p}$为给定系数矩阵. 数值实验表明已有的Majorization算法虽可行, 但收敛速度缓慢且精度不高. 本文从黎曼流形的角度重新研究该问题, 基于Stiefel流形的几何性质, 构造一类黎曼非单调共轭梯度迭代求解算法, 并给出算法收敛性分析.数值实验和数值比较验证所提出的算法对于问题模型是高效可行的.     

Investigation of Relationships between Grain Structure and Inhomogeneous Deformation by Means of Laboratory-Based Multimodal X-Ray Tomography: Strain Accuracy Analysis

Experimental Mechanics - The internal strain distribution developing during plastic deformation is important for understanding the mechanical properties of polycrystalline materials. Such...     

A Nonclinical Spectroscopic Approach for Diagnosing Covid-19: A Concise Perspective

Journal of Applied Spectroscopy - With the COVID-19 outbreak, many challenges are posed before the scientific world to curb this pandemic. The diagnostic testing, treatment, and vaccine development...     

k-Hankel Gabor Transform and Its Applications to the Theory of Localization Operators

Analysis Mathematica - We introduce and study the k-Hankel Gabor transform. We investigate the localization operators for this transform. In particular, we study their trace class properties and we...     

Virtual Field Characterization for Ratcheting Effect Under Cyclic Loading

Experimental Mechanics - Ratcheting is an important mechanical behavior of metals and alloys, which is caused by the repeated accumulations of tensile and compressive strain in circle load....     

Vacuum Conditions and the Lifetime of a Single-Charged Helium Ion Beam in the Booster Synchrotron of the NICA (First Run)

JETP Letters - The results of the first run (December 2020) for the commissioning of the new superconducting synchrotron Booster at the Joint Institute for Nuclear Research are presented. Vacuum...     

Nonlinear Optical Properties of Novel Metallophthalocyanines

Journal of Applied Spectroscopy - Detailed measurements of nonlinear optical properties and optical limiting for four phthalocyanine (Pc) derivatives (PcCo, PcCu, PcMn, and PcSi) are reported. The...     

Stability and control of radial deployment of electric solar wind sail

Nonlinear Dynamics - The paper studies the stability and control of radial deployment of an electric solar wind sail with the consideration of high-order modes of elastic tethers. The electric...     

Secondary Metabolites of Litchi chinensis

Chemistry of Natural Compounds -