• Title/Summary/Keyword: Eigenvector Method

Search Result 159, Processing Time 0.022 seconds

Efficient Algorithms for Computing Eigenpairs of Hermitian Matrices (Hermitian 행렬의 고유쌍을 계산하는 효율적인 알고리즘)

  • Jeon, Chang-Wan;Kim, Hyung-Jung;Lee, Jang-Gyu
    • Proceedings of the KIEE Conference
    • /
    • 1995.07b
    • /
    • pp.729-732
    • /
    • 1995
  • This paper presents a Generalized Iteration (GI) which includes power method, inverse power method, shifted inverse power method, and Rayleigh quotient iteration (RQI), and modified RQI (MRQI). Furthermore, we propose a GI-based algorithm to find arbitrary eigenpairs for Hermitian matrices. The proposed algorithm appears to be much faster and more accurate than the valuable generalized MRQI of Hu (GMRQI-Hu). The idea of GI is also employed to speed up the GMRQI-Hu and we propose a modified version of Hu's GMRQI (GMRQI-Hu-mod) which is improved in the convergence rate. Some numerical simulation results are presented to confirm our contributions

  • PDF

Influence of clamped-clamped boundary conditions on the mechanical stress, strain and deformation analyses of cylindrical sport equipment

  • Yuhao Yang;Mohammad Arefi
    • Geomechanics and Engineering
    • /
    • v.35 no.5
    • /
    • pp.465-473
    • /
    • 2023
  • The higher order shear deformable model and an exact analytical method is used for analytical bending analysis of a cylindrical shell subjected to mechanical loads, in this work. The shell is modelled using sinusoidal bivariate shear strain theory, and the static governing equations are derived using changes in virtual work. The eigenvalue-eigenvector method is used to exactly solve the governing equations for a constrained cylindrical shell The proposed kinematic relation decomposes the radial displacement into bending, shearing and stretching functions. The main advantage of the method presented in this work is the study of the effect of clamping constraints on the local stresses at the ends. Stress, strain, and deformation analysis of shells through thickness and length.

A New Method for Monitoring Local Voltage Stability using the Saddle Node Bifurcation Set in Two Dimensional Power Parameter Space

  • Nguyen, Van Thang;Nguyen, Minh Y.;Yoon, Yong Tae
    • Journal of Electrical Engineering and Technology
    • /
    • v.8 no.2
    • /
    • pp.206-214
    • /
    • 2013
  • This paper proposes a new method for monitoring local voltage stability using the saddle node bifurcation set or loadability boundary in two dimensional power parameter space. The method includes three main steps. First step is to determine the critical buses and the second step is building the static voltage stability boundary or the saddle node bifurcation set. Final step is monitoring the voltage stability through the distance from current operating point to the boundary. Critical buses are defined through the right eigenvector by direct method. The boundary of the static voltage stability region is a quadratic curve that can be obtained by the proposed method that is combining a variation of standard direct method and Thevenin equivalent model of electric power system. And finally the distance is computed through the Euclid norm of normal vector of the boundary at the closest saddle node bifurcation point. The advantage of the proposed method is that it gets the advantages of both methods, the accuracy of the direct method and simple of Thevenin Equivalent model. Thus, the proposed method holds some promises in terms of performing the real-time voltage stability monitoring of power system. Test results of New England 39 bus system are presented to show the effectiveness of the proposed method.

Non-redundant Precoding Based Blind Channel Estimation Scheme for OFDM Systems (OFDM 시스템에서 비중복 프리코딩을 이용한 미상 채널 추정 방법)

  • Seo, Bang-Won
    • The Journal of Korean Institute of Communications and Information Sciences
    • /
    • v.37 no.6A
    • /
    • pp.450-457
    • /
    • 2012
  • For orthogonal frequency-division multiplexing (OFDM) systems, we propose a blind channel estimation scheme based on non-redundant precoding. In the proposed scheme, a modified covariance matrix is first obtained by dividing the covariance matrix of the received signal vector by the precoding matrix element-by-element. Then, the channel vector is estimated as an eigenvector corresponding to the largest eigenvalue of the modified covariance matrix. The eigenvector can be obtained by power method with low computational complexity instead of the complicated eigenvalue decomposition. We analytically derive a mean square error (MSE) of the proposed channel estimation scheme and show that the analysis result coincides well with the simulation result. Also, simulation results show that the proposed scheme has better MSE and bit error rate (BER) performance than conventional channel estimation schemes.

Computational Analysis of PCA-based Face Recognition Algorithms (PCA기반의 얼굴인식 알고리즘들에 대한 연산방법 분석)

  • Hyeon Joon Moon;Sang Hoon Kim
    • Journal of Korea Multimedia Society
    • /
    • v.6 no.2
    • /
    • pp.247-258
    • /
    • 2003
  • Principal component analysis (PCA) based algorithms form the basis of numerous algorithms and studies in the face recognition literature. PCA is a statistical technique and its incorporation into a face recognition system requires numerous design decisions. We explicitly take the design decisions by in-troducing a generic modular PCA-algorithm since some of these decision ate not documented in the literature We experiment with different implementations of each module, and evaluate the different im-plementations using the September 1996 FERET evaluation protocol (the do facto standard method for evaluating face recognition algorithms). We experiment with (1) changing the illumination normalization procedure; (2) studying effects on algorithm performance of compressing images using JPEG and wavelet compression algorithms; (3) varying the number of eigenvectors in the representation; and (4) changing the similarity measure in classification process. We perform two experiments. In the first experiment, we report performance results on the standard September 1996 FERET large gallery image sets. The result shows that empirical analysis of preprocessing, feature extraction, and matching performance is extremely important in order to produce optimized performance. In the second experiment, we examine variations in algorithm performance based on 100 randomly generated image sets (galleries) of the same size. The result shows that a reasonable threshold for measuring significant difference in performance for the classifiers is 0.10.

  • PDF

A Parallel Algorithm of Davidson Method for Solving and Electomagnetic Problem (전자장문제를 위한 Davidson 방번의 병렬화)

  • Kim, Hyong Joong;Zhu, Yu
    • Journal of Industrial Technology
    • /
    • v.17
    • /
    • pp.255-260
    • /
    • 1997
  • The analysis of eigenvalue and eigenvector is a crucial procedure for many electromagnetic computation problems. Although it is always the case in practice that only selected eigenpairs are needed, computation of eigenpair still seems to be a time-consuming task. In order to compute the eigenpair more quickly, there are two resorts: one is to select a good algorithm with care and another is to use parallelization technique to improve the speed of the computing. In this paper, one of the best eigensolver, the Davidson method, is parallelized on a cluster of workstations. We apply this scheme to a ridged waveguide design problem and obtain promising linear speedup and scalability.

  • PDF

Optimal Selection of Master States for Order Reduction (동적시스템의 차수 줄임을 위한 주상태의 최적선택)

  • 오동호;박영진
    • Journal of KSNVE
    • /
    • v.4 no.1
    • /
    • pp.71-82
    • /
    • 1994
  • We propose a systematic method to select the master states, which are retained in the reduced model after the order reduction process. The proposed method is based on the fact that the range space of right eigenvector matrix is spanned by orthogonal base vectors, and tries to keep the orthogonality of the submatrix of the base vector matrix as much as possible during the reduction process. To quentify the skewness of that submatrix, we define "Absolute Singularity Factor(ASF)" based on its singular values. While the degree of observability is concerned with estimation error of state vector and up to n'th order derivatives, ASF is related only to the minimum state estimation error. We can use ASF to evaluate the estimation performance of specific partial measurements compared with the best case in which all the state variables are identified based on the full measurements. A heuristic procedure to find suboptimal master states with reduced computational burden is also proposed. proposed.

  • PDF

Speaker Identification Using Greedy Kernel PCA (Greedy Kernel PCA를 이용한 화자식별)

  • Kim, Min-Seok;Yang, Il-Ho;Yu, Ha-Jin
    • MALSORI
    • /
    • no.66
    • /
    • pp.105-116
    • /
    • 2008
  • In this research, we propose a speaker identification system using a kernel method which is expected to model the non-linearity of speech features well. We have been using principal component analysis (PCA) successfully, and extended to kernel PCA, which is used for many pattern recognition tasks such as face recognition. However, we cannot use kernel PCA for speaker identification directly because the storage required for the kernel matrix grows quadratically, and the computational cost grows linearly (computing eigenvector of $l{\times}l$ matrix) with the number of training vectors I. Therefore, we use greedy kernel PCA which can approximate kernel PCA with small representation error. In the experiments, we compare the accuracy of the greedy kernel PCA with the baseline Gaussian mixture models using MFCCs and PCA. As the results with limited enrollment data show, the greedy kernel PCA outperforms conventional methods.

  • PDF

Matched Field Processing: Ocean Experimental Data Analysis Using Feature Extraction Method (실 해상 실험 데이터를 이용한 정합장 처리에서의 특성치 추출 기법 분석)

  • Kim Kyung Seop;Seong Woo Jae;Song Hee Chun
    • The Journal of the Acoustical Society of Korea
    • /
    • v.24 no.1E
    • /
    • pp.21-27
    • /
    • 2005
  • Environmental mismatch has been one of important issues discussed in matched field processing for underwater source detection problem. To overcome this mismatch many algorithms professing robustness have been suggested. Feature extraction method (FEM) [Seong and Byun, IEEE Journal of Oceanic Engineering, 27(3), 642-652 (2002)] is one of robust matched field processing algorithms, which is based on the eigenvector estimation. Excluding eigenvectors of replica covariance matrix corresponding to large eigenvalues and forming an incoherent subspace of the replica field, the processor is formulated similarly to MUSIC algorithm. In this paper, by using the ocean experimental data, processing results of FEM and MVDR with white noise constraint (WNC) are presented for two levels of multi-tone source. Analysis of eigen-space of CSDM and FEM performance are also presented.

Multiple-Criteria Decision-Making Using Sectional Supermatrix

  • Kameya, Nagayuki;Miyagi, Hayao;Taira, Naoyuki;Yamashita, Katsumi
    • Proceedings of the IEEK Conference
    • /
    • 2002.07b
    • /
    • pp.838-840
    • /
    • 2002
  • Presently, Analytic Network Process which evaluates man's intention and offers decision-making support is capturing the spotlight. It originates in the ability of Analytic Network Process to treat various decision-making support system. However, no detailed reference is available when dealing with the group case. This paper examines the technique, which can also cope with the group decision-making support system, and describes the validity of the technique. A characteristic feature of the proposed technique is that it can detect a group's intention in a given section, and it decomposes the sectional supermatrix into a small supermatrix and a large one. A general supermatrix treats the convergence value by taking the limiting process method of the power of an evaluation value. On the other hand, when a supermatrix has nonnegative value, it can easily be solved by the eigenvector method. The decomposition of the supermatrix has been considered in this work.

  • PDF