Eigenvalue Decomposition Method Research Articles

Large-scale wave-front reconstruction for adaptive optics systems by use of a recursive filtering algorithm

We propose a new recursive filtering algorithm for wave-front reconstruction in a large-scale adaptive optics system. An embedding step is used in this recursive filtering algorithm to permit fast methods to be used for wave-front reconstruction on an annular aperture. This embedding step can be used alone with a direct residual error updating procedure or used with the preconditioned conjugate-gradient method as a preconditioning step. We derive the Hudgin and Fried filters for spectral-domain filtering, using the eigenvalue decomposition method. Using Monte Carlo simulations, we compare the performance of discrete Fourier transform domain filtering, discrete cosine transform domain filtering, multigrid, and alternative-direction-implicit methods in the embedding step of the recursive filtering algorithm. We also simulate the performance of this recursive filtering in a closed-loop adaptive optics system.

Application of Imaging Techniques to Geometry Analysis of Aggregate Particles

This paper presents image analysis techniques by which to characterize the texture, angularity, and form of aggregate particles used in highway construction and geotechnical applications. For texture analysis, wavelet decomposition in gray scale images of particles is performed. The results demonstrate that multiscale wavelet representation is a powerful tool by which to capture the texture and to differentiate true texture from false texture caused by variations of natural color on a particle surface. Angularity and form analyses of particles are done using binary images. A gradient-based method is employed to describe angularity. This method is shown to differentiate between particles with different angularity characteristics. Form analysis of the particles includes computing the shape factor and sphericity index, which are based on measurements of the shortest, intermediate, and longest axis of the particle. Particle thickness is measured using the feature of an autofocus microscope. The width and length are calculated by an eigenvalue decomposition method of two-dimensional particle projections. Details of an interactive software developed to compute the different aggregate shape factors are discussed. The results indicate that these calculated values of the particle dimensions match very closely the values measured manually using a digital caliper.

Design and analysis of a 2-D eigenspace-based interference canceller

This paper deals with the problem of eigenspace-based interference cancellation using a two-dimensional (2-D) rectangular array. An efficient 2-D signal blocking technique is presented to remove the desired signal from the received array data. In conjunction with the 2-D signal blocking technique, a positive definite matrix is further constructed and used to compensate the effect of the signal blocking operation on the sensor noise received by a 2-D eigenspace-based interference canceller (EIC). Therefore, the interference subspace required for computing the optimal weight vector of the designed 2-D EIC can be obtained by simply using conventional eigenvalue decomposition methods instead of any complicated generalized eigenvalue decomposition methods. The performances of the designed 2-D EIC under finite samples and steering angle error are also evaluated. The developed theoretical results are confirmed by several simulation examples.

Simplifying fuzzy rule-based models using orthogonal transformation methods

An important issue in fuzzy-rule-based modeling is how to select a set of important fuzzy rules from a given rule base. Even though it is conceivable that removal of redundant or less important fuzzy rules from the rule base can result in a compact fuzzy model with better generalizing ability, the decision as to which rules are redundant or less important is not an easy exercise. In this paper, we introduce several orthogonal transformation-based methods that provide new or alternative tools for rule selection. These methods include an orthogonal least squares (OLS) method, an eigenvalue decomposition (ED) method, a singular value decomposition and QR with column pivoting (SVD-QR) method, a total least squares (TLS) method, and a direct singular value decomposition (D-SVD) method. A common attribute of these methods is that they all work on a firing strength matrix and employ some measure index to detect the rules that should be retained and eliminated. We show the performance of these methods by applying them to solving a nonlinear plant modeling problem. Our conclusions based on analysis and simulation can be used as a guideline for choosing a proper rule selection method for a specific application.

Parallel singular value decomposition of complex matrices using multidimensional CORDIC algorithms

The singular value decomposition (SVD) of complex matrices is computed in a highly parallel fashion on a square array of processors using Kogbetliantz's analog of Jacobi's eigenvalue decomposition method. To gain further speed, new algorithms for the basic SVD operations are proposed and their implementation as specialized processors is presented. The algorithms are 3-D and 4-D extensions of the CORDIC algorithm for plane rotations. When these extensions are used in concert with an additive decomposition of 2/spl times/2 complex matrices, which enhances parallelism, and with low resolution rotations early on in the SVD process, which reduce operation count, a fivefold speedup can be achieved over the fastest alternative approach.

Laboratory information system for nuclear magnetic resonance relaxometry in biomedical materials (NMR LIS). II. Data analysis

Data analysis modules for Nuclear Magnetic Resonance Relaxometry LIS are described. Since the experimental NMR results from biomedical samples often exhibit complex structure that arises from complexity of tissue, the analysis methods focus on search, investigation, and evaluation of complex multiexponential relaxation features. Two algorithms have been implemented: an enhanced spin grouping method that is based on a multiexponential curve stripping algorithm, and an eigenvalue decomposition method, implemented as modified DISCRETE program.

Calculation and Experimental Verification of Solute Retention in Liquid Chromatography Using Binary Eluents

Abstract The chromatographic transport problem is a kinematic wave problem that generally leads to a set of coupled, nonlinear partial differential equations. In the linear elution mode of chromatography an approximation can be made which allows linearization of the set of equations and hence solution by the matrix eigenvalue decomposition method. To make the solution explicit, an expression for a multicomponent distribution isotherm is required. Generally, Langmuir isotherms are used for this purpose. In this work a recently published multicomponent isotherm, that can be derived from first principles, is applied to the problem. For the case of binary eluents the capacity factors and peak compositions of both system peaks and analyte peaks are calculated using the elution mode approximation and the isotherm referred to above. Experimental results pertain to the ion-exchange separation of alkali ions. A good agreement between calculated and measured quantities is observed. An important consequence of interactions among sample and eluent constituents for the practice of chromatography lies in the field of indirect detection. The possibility of universal detection in LC is briefly discussed.

Estimation of systems of equations subject to curvature constraints

Two computationally manageable estimation procedures for maintaining curvature constraints are compared. Using an efficient nonlinear optimizing algorithm, the well-known Cholesky factorization is compared with the eigenvalue decomposition method for estimating a system of input demand and output supply equations. Statistical tests are provided. The Cholesky factorization is superior when efficient optimizers are used. The eigenvalue decomposition may become a better choice when the user is limited to less efficient algorithms.