非齐次对称特征值问题

所谓非齐次对称特征值问题就是给定对称矩阵A,一个向量b,求实数λ和向量X使得AX=λX+b并且‖×‖_2=1,则称λ为非齐次特征值,相应的向量X称为非齐次特征向量、本文讨论了非齐次对称特征值问题解的存在性及解的个数;描述了求解非齐次对称特征值问题的数值方法.     

Design of experiments for Quick U-building method for building energy performance measurement

Quick U-building (QUB) is a method for short time measurement of energy performance of buildings, typically one night. It uses the indoor air temperature response to the power delivered to the indoor air by electric heaters. This paper introduces a method for estimating the expected measurement error as a function of the amplitude and the time duration of the input signal based on the decomposition of the time response of a state-space model into a sum of exponentials by using the eigenvalues of the state matrix. It is shown that the buildings have a group of dominant time constants, which gives an exponential response, and many very short and very large time constants, which have a small influence on the response. The analysis of the eigenvalues demonstrates that the QUB experiment may be done in a rather short time as compared with the largest time constant of the building.     

Explicit form for impedance of cauer networks

In this paper a new procedure is established to obtain in closed form the poles and zeros of the impedance function of a first Cauer Network. The technique involves the continued fraction representation of the corresponding Laplace transform as a rational function whose numerators and denominators can be represented by tridiagonal determinants.     

An efficient preconditioning scheme for plane-wave-based electronic structure calculations

We propose a preconditioning scheme for diagonalizing large Hamiltonian matrices arising in first-principles plane-wave pseudopotential calculations. The new scheme is based on the Neumann expansion for the inverse, shifted Hamiltonian from which only a nonlocal part is omitted. The preconditioner is applied to a gradient vector using the fast Fourier transformation technique. In the framework of the Davidson-type diagonalization algorithm, we have found the present preconditioning scheme to be more efficient than widely accepted diagonal scaling methods.     

Bipartite isoperimetric graph partitioning for data co-clustering

Data co-clustering refers to the problem of simultaneous clustering of two data types. Typically, the data is stored in a contingency or co-occurrence matrix C where rows and columns of the matrix represent the data types to be co-clustered. An entry C _ij of the matrix signifies the relation between the data type represented by row i and column j. Co-clustering is the problem of deriving sub-matrices from the larger data matrix by simultaneously clustering rows and columns of the data matrix. In this paper, we present a novel graph theoretic approach to data co-clustering. The two data types are modeled as the two sets of vertices of a weighted bipartite graph. We then propose Isoperimetric Co-clustering Algorithm (ICA)—a new method for partitioning the bipartite graph. ICA requires a simple solution to a sparse system of linear equations instead of the eigenvalue or SVD problem in the popular spectral co-clustering approach. Our theoretical analysis and extensive experiments performed on publicly available datasets demonstrate the advantages of ICA over other approaches in terms of the quality, efficiency and stability in partitioning the bipartite graph.     

一种基于特征向量的高效虚拟现实辐射度算法

辐射度技术对于具有真实感的图像的合成十分重要。提出了一种基于特征向量的虚拟现实环境中辐射度计算的新方法。该方法采用了并行计算方法计算形状因子矩阵的特征值和特征向量,进而实现对虚拟现实环境中的辐射度进行高效的计算。其性能总体评价结果显示该方法显著降低了复杂环境中集群计算机系统的有效计算时间,提高了计算效率和加速比。其成果可广泛应用在图像处理、人机交互、可视化、虚拟现实等领域。     

高维度满速率的宏分集空时编码方案

为了适应宏分集传输中高天线数的要求,提出一种高维度满速率的空时编码方案. 这种高维度编码可以达到满速率传输,且其最大似然译码复杂度可控,只需对(发射天线数/2)个实数符号联合最大似然译码. 对该编码的等效信道相关矩阵进行分析后得出结论：等效信道右奇异矩阵为常数矩阵. 提出一种具有单符号线性译码复杂度的无反馈要求的预处理传输机制,使译码复杂度大大降低. 仿真结果表明,相比于最小译码复杂度编码以及其他宏分集传输方案,如循环延迟分集,高维度满速率编码方案的性能有一定提升.     

广义模糊矩阵的标准特征向量

讨论了广义模糊矩阵,即"取大-三角模"复合意义下模糊矩阵的标准特征向量的代数结构.给出了模糊矩阵存在标准特征向量的充分必要条件,建立了标准特征向量的代数表示.     

Multispectral image compression using eigenregion-based segmentation

In the study, a novel segmentation technique is proposed for multispectral satellite image compression. A segmentation decision rule composed of the principal eigenvectors of the image correlation matrix is derived to determine the similarity of image characteristics of two image blocks. Based on the decision rule, we develop an eigenregion-based segmentation technique. The proposed segmentation technique can divide the original image into some proper eigenregions according to their local terrain characteristics. To achieve better compression efficiency, each eigenregion image is then compressed by an efficient compression algorithm eigenregion-based eigensubspace transform (ER-EST). The ER-EST contains 1D eigensubspace transform (EST) and 2D-DCT to decorrelate the data in spectral and spatial domains. Before performing EST, the dimension of transformation matrix of EST is estimated by an information criterion. In this way, the eigenregion image may be approximated by a lower-dimensional components in the eigensubspace. Simulation tests performed on SPOT and Landsat TM images have demonstrated that the proposed compression scheme is suitable for multispectral satellite image.     

Higher order eigensensitivity analysis of damped systems with repeated eigenvalues

A simplified method for the computation of first-, second- and higher-order derivatives of eigenvalues and eigenvectors associated with repeated eigenvalues is presented. Adjacent eigenvectors and orthonormal conditions are used to compose an algebraic equation. The algebraic equation which is developed can be used to compute derivatives of eigenvalues and eigenvectors simultaneously. Since the coefficient matrix in the proposed algebraic equation is non-singular, symmetric and based on N-space, it is numerically stable and very efficient compared to previous methods. To verify the efficiency of the proposed method, the finite element model of the cantilever beam and a mechanical system in the case of a non-proportionally damped system are considered.