in this paper, the rayleigh's quotient and the inverse vector iteration method are presented. the latter approach helps to obtain the natural frequencies and mode shapes of a structure. inverse vector iteration method with shifting enables to determine the higher modes. some basic theorems of linear algebra are presented and extended to study the free vibration of structures. the variation...

In coupled learning rules for principal component analysis, eigenvectors and eigenvalues are simultaneously estimated in a coupled system of equations. Coupled single-neuron rules have favorable convergence properties. For the estimation of multiple eigenvectors, orthonormalization methods have to be applied, either full Gram-Schmidt orthonormalization, its first-order approximation as used in ...

the principle of dimensionality reduction with pca is the representation of the dataset ‘x’in terms of eigenvectors ei ∈ rn  of its covariance matrix. the eigenvectors oriented in the direction with the maximum variance of x in rn carry the most      relevant information of x. these eigenvectors are called principal components [8]. assume that n images in a set are originally represented in mat...

aims: the internal unit and icu of hospitals are a suitable environment for growing of bacteria such as staphylococcus epidermidis and pseudomonas, acinetobacter. the aim of our study was to evaluate the effect of different disinfectants on bacteria isolated from the surface of hospitals in isfahan. instrument & methods: in this study, 200 samples were randomly selected from different parts of ...

In this part, we discuss some practical methods for computing eigenvalues and eigenvectors of matrices. Needless to say, we completely avoid trying to solve (or even write down) the characteristic polynomial equation. The very basic power method and its variants, which is based on linear iteration, is used to effectively approximate selected eigenvalues. To determine the complete system of eige...

A real symmetric matrix of order n has a full set of orthogonal eigenvectors. The most used approach to compute the spectrum of such matrices reduces first the dense symmetric matrix into a symmetric structured one, i.e., either a tridiagonal matrix [2, 3] or a semiseparable matrix [4]. This step is accomplished in O(n) operations. Once the latter symmetric structured matrix is available, its s...

The recent emergence of the discrete fractional Fourier transform has spurred research activity aiming at generating Hermite-Gaussian-like (HGL) orthonormal eigenvectors of the discrete Fourier transform (DFT) matrix F. By exploiting the unitarity of matrix F – resulting in the orthogonality of its eigenspaces pertaining to the distinct eigenvalues – the problem decouples into finding orthonorm...

The principle of dimensionality reduction with PCA is the representation of the dataset ‘X’in terms of eigenvectors ei ∈ RN  of its covariance matrix. The eigenvectors oriented in the direction with the maximum variance of X in RN carry the most      relevant information of X. These eigenvectors are called principal components [8]. Ass...

The principle of dimensionality reduction with PCA is the representation of the dataset ‘X’in terms of eigenvectors ei ∈ RN  of its covariance matrix. The eigenvectors oriented in the direction with the maximum variance of X in RN carry the most      relevant information of X. These eigenvectors are called principal components [8]. Ass...

Kernel related algorithms, including spectral techniques, have found their use in a variety of fields. However, the construction and eigendecomposition of the Gram matrix necessitate efforts to reduce the computational overhead. One particular interesting approach used for this purpose is Nyström method. In this paper, we study the sampling problem for Nyström method. To measure the quality of ...