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Bananas are, in Uganda primarily, grown for domestic consumption and regional trade. Production is constrained by several factors such as declining soil fertility, pests and disease, and erratic rainfall. Tissue culture banana were introduced partly to solve some of the challenges in banana production, though uptake of such technologies by smallholder farmers is still low. A survey on plant parasitic nematodes, banana weevils, and selected soil factors was done to analyse their effect on the abundance of tissue culture banana (TCB) and non-tissue culture banana (NTCB). Soil and banana root samples were collected from heterogeneous on-farm orchard conditions in smallholder farms. Composite banana root samples and composite soil samples were collected from banana orchards already established by farmers. A total of 1,280 genets from 20 orchards were obtained. Composite soil samples were analysed for pH, potassium, phosphorus, nitrogen, and organic matter. Endo-parasitic Helicotylenchus multinctus, Platylenchus goodeyi, Radopholous similis and Meloidogyne spp were isolated from the composite root samples. Banana weevils were captured using the disc-on-stamp and split-pseudo stem traps. Redundancy Analysis (RDA) and logistic regression were run to ascertain the relationship between variations in biotic [Nematodes and weevils] and abiotic [pH, K, Av.P, N, and OM] factors affecting the abundance of the banana type. Canonical eigenvalues showed that both biotic and abiotic variables significantly affected the abundance of TCB and NTCB banana types. Abundance of TCB was influenced by the banana weevil (P Key words: abundance, banana weevil, nematodes, eigenvalues, interactions, tissue culture, genet, heterogeneous, BACKGROUND The banana is a perennial monocotyledonous herb whose importance and level of production are vindicated by bananas' distinctive support to food, feed, and fuel and, fibre production in East [...]

We describe and analyze a randomized homotopy algorithm for the Hermitian eigenvalue problem. Given an n x n Hermitian matrix A, the algorithm returns, almost surely, a pair (λ, v) which approximates, in a very strong sense, an eigenpair of A. We prove that the expected cost of this algorithm, where the expectation is both over the random choices of the algorithm and a probability distribution on the input matrix A, is O([n.sup.6]), that is, cubic on the input size. Our result relies on a cost assumption for some pseudorandom number generators whose rationale is argued by us. Keywords Eigenpair computation * Homotopy methods * Complexity analysis Mathematics Subject Classification 65F15, 1 Introduction Numerical linear algebra is arguably the best developed part of numerical analysis. This is not surprising since all numerical computations ultimately reduce to linear algebra, and this feature [...]

We study a weaker formulation of the nullspace property which guarantees recovery of sparse signals from linear measurements by [l.sub.1] minimization. We require this condition to hold only with high [...]

This article considers estimation and applications of constrained and partially constrained factor models when the dimension of explanatory variables is high. Both the classical and approximate factor models are investigated. For estimation, we employ both the maximum likelihood and least squares methods. We show that the least squares estimation is based on constrained principal component analysis and provides consistent estimates for the model under certain conditions. The normality condition is not used in the derivation. We then propose likelihood ratio statistics to test the adequacy of factor constraints. The test statistic is developed under the normality assumption, but simulation results show that it continues to perform well even if the underlying distribution is Student-t. The constraints are useful tools to incorporate prior information or substantive theory in applications of factor models. In addition, the constraints also serve as a statistical tool to obtain parsimonious econometric models for forecasting, to simplify the interpretations of common factors, and to reduce the dimension. We use simulation and real examples to investigate the performance of constrained estimation in finite samples and to highlight the importance of noise-to-signal ratio in factor analysis. Finally, we compare the constrained model with its unconstrained counterpart both in estimation and in forecasting. This article has supplementary material online. KEY WORDS: Approximate factor model; Constrained principal component analysis; Eigenvalues; Least squares estimation; Likelihood ratio test; Noise-to-signal ratio.

An eigenvalue analysis numerical technique for curved closed waveguiding structures loaded with inhomogeneous and/or anisotropic materials is presented. For this purpose, a frequency-domain finite-difference method is developed for a general orthogonal curvilinear coordinate system. The main strength of the technique is the accurate modeling of curved transverse boundaries, as well as curved geometries along the propagation direction, under certain limitations for the latter. This feature avoids the necessity of a fine mesh, while it retains a high accuracy and it is free of any staircase effects. In general, the proposed method shares the finite-element technique capabilities in modeling complex boundaries, while it preserves the finite-difference convenience in handling inhomogeneous and anisotropic material loadings. The resulting eigenvalue-based problem is solved using the Arnoldi algorithm, which exploits the system matrix sparcity and the overall technique is robust, unconditionally stable with minimal computational and memory requirements. Numerical results are validated against analytical results and results from 3-D commercial electromagnetic simulators. Finally, novel results are also given. Index Terms--Conformal structures, curved waveguides, eigenvalues, finite-difference methods, waveguide bends.

In this paper, the problem of evaluating resonant frequencies of arbitrarily shaped substrate integrated waveguide resonators is considered. Resonances are found regarding them as nonlinear eigenvalues of the operator describing the scattering by metallic posts in a parallel plate waveguide. Nonlinear eigenvalues are usually computed by singular value decomposition. In order to save computational time, we propose an alternative approach derived by some general consideration on the theory of nonlinear eigenvalue problems in the discrete case. Results on rectangular, circular, and elliptical cavities are presented and compared with High Frequency Structure Simulator software package simulations. It is shown that the proposed method is efficient and accurate. Index Terms--Microwave resonators, nonlinear eigenvalue problems, singular value decomposition (SVD), substrate integrate waveguide (SIW).

The Jacobi-Davidson method is very attractive for the large-scale finite element simulation of electromagnetic cavity problems, because it just requires approximate solutions to some auxiliary systems of linear equations, which are easily obtained by iterative solvers. Moreover, rates of convergence are quadratic to cubic. In consequence, the time spent within the pre-asymptotic region at the early stages of the iteration may have strong impact on overall performance, particularly when the number of eigenvalues sought is small. Therefore, we propose a startup procedure that utilizes p hierarchical finite element spaces to reduce the cost of bridging the pre-asymptotic region. Index Terms--Eigenvalues and eigenfunctions, electromagnetic fields, finite element methods, numerical analysis.

An algorithm is presented for direction-of-arrival (DOA) estimation in the presence of unknown mutual coupling based on the generalized eigenvalues utilizing signal subspace eigenvectors (GEESE) algorithm for uniform linear array (ULA). It is not an iterative algorithm, and a spectral peak search is not required. The DOA can be accurately estimated without any calibration sources since the effects of mutual coupling can be eliminated by the inherent mechanism of the proposed algorithm. An algorithm for estimating the mutual coupling coefficients is also proposed. Simulation results demonstrate the effectiveness of the proposed algorithms.

This paper focuses on the systematic optimal tuning of the power system stabilizer (PSS), which can improve the system damping performance immediately following a large disturbance. As the PSS consists of both linear parameters (such as the gain and time constant) and nonsmooth nonlinear parameters (such as saturation limits of the PSS), two methods are applied for the optimal tuning of all parameters. One is to use the optimization technique based on the Hessian matrix estimated by the feedforward neural network, which identifies the first-order derivatives obtained by the trajectory sensitivities, for the nonlinear parameters. Moreover, the other is to use the eigenvalue analysis for the linear parameters. The performances of parameters optimized by the proposed method are evaluated by the case studies based on time-domain simulation and real-time hardware implementation. Index Terms--Eigenvalue analysis, feedforward neural network (FFNN), Hessian matrix estimation, hybrid system, nonlinearities, parameter optimization, power system stabilizer (PSS), trajectory sensitivities.

Rational models must be passive in order to ensure stable time domain simulations. The assessment of passivity properties is usually done via a Hamiltonian matrix that is associated with the state-space model, allowing precise characterization of passivity violations from its imaginary eigenvalues. The calculation of eigenvalues can be time consuming for large models as the matrix size is equal to twice the number of model states. In this paper, we derive for S-parameter models a new test matrix which is only half the size of the Hamiltonian matrix. This leads to savings in the eigenvalue computation time by a factor of nearly eight. The new test matrix takes into account that the model is symmetrical, in pole-residue form. Its application is demonstrated by three examples: a microwave filter, a package, and a synthetic model. Index Terms--Hamiltonian matrix, macromodel, passivity, passivity assessment, rational model, S-parameters.

This paper introduces a new technique for robust aeroelastic analysis that extends standard linear flutter analysis to take deterministic uncertainty and variation into account. The basic principle of the proposed [mu]-p method is to exploit structured-singular-value (or [mu]) analysis to investigate if the system uncertainties can make the flutter determinant zero for a given flutter eigenvalue p. This makes it possible to compute regions of feasible eigenvalues in the complex plane as well as extreme eigenvalues that can he used to predict damping bounds and perform robust flutter analysis. The capability to predict damping bounds at subcritical flight conditions is a very attractive feature of the new method, as flight testing is rarely taken to the flutter point. The [mu]-p formulation also opens up new possibilities to bound the magnitude of the system uncertainties based on frequency and/or damping estimates from flight testing. In the final part of the paper, the [mu]-p framework is successfully applied to perform robust aeroelastic analysis of a low-speed wind-tunnel model. DOI: 10.2514/1.35859

This note proposes an improved eigenvalue-counting method based on the argument principle by introducing Rombouts' algorithm, which is a stable, efficient, and accurate algorithm to calculate the coefficients of the characteristic polynomial of a general square matrix. In addition, this note comprehensively investigates the effectiveness of the proposed method from the viewpoint of the practical consideration by comparing with the modified Sturm sequence property-based counting method which has been recently developed and also known as the well-proven method. In this note, the operation counts in each method are carefully compared and numerically verified. According to analytical and numerical comparison, the argument principle-based counting method is much better than the modified Sturm sequence property-based method from a practical point of view, even if the latter method is much well-established one theoretically. CE Database subject headings: Eigenvalues; Damping; Algorithms.

Abstract Eigenvalue problem of SC matrices with the form ααT and matrices sum with the form [αα.sup.T] (α ζ [R.sup.n]) is discussed, and a structure of orthogonal matrices of SC [...]

Bayesian nonparametric models are widely and successfully used for statistical prediction. While posterior consistency properties are well studied in quite general settings, results have been proved using abstract concepts such as metric entropy, and they come with subtle conditions which are hard to validate and not intuitive when applied to concrete models. Furthermore, convergence rates are difficult to obtain. By focussing on the concept of information consistency for Bayesian Gaussian process (GP)models, consistency results and convergence rates are obtained via a regret bound on cumulative log loss. These results depend strongly on the covariance function of the prior process, thereby giving a novel interpretation to penalization with reproducing kernel Hilbert space norms and to commonly used covariance function classes and their parameters. The proof of the main result employs elementary convexity arguments only. A theorem of Widom is used in order to obtain precise convergence rates for several covariance functions widely used in practice. Index Terms--Bayesian prediction, eigenvalue asymptotics, Gaussian process, information consistency, nonparametric statistics, online learning, posterior consistency, regret bound.

This paper uses an incremental matrix expansion approach to derive asymptotic eigenvalue distributions (a.e.d.s) of sums and products of large random matrices. We show that the result can be derived directly as a consequence of two common assumptions, and matches the results obtained from using Rand S-transforms in free probability theory. We also give a direct derivation of the a.e.d, of the sum of certain random matrices which are not free. This is used to determine the asymptotic signal-to-interference-ratio of a multiuser code-division multiple-access (CDMA) system with a minimum mean-square error linear receiver. Index Terms--Code-division multiple access (CDMA), free probability, large system, minimum mean square error (MMSE), R-transform, S-transform.

A reduced-rank minimum description length (MDL) method is presented for the enumeration of the incident waves impinging on a uniform linear array (ULA). The proposed method is found to be better than the traditional MDL methods in detection performance and computational complexity.

An eigenvector-based algorithm for multidimensional frequency estimation with finite date snapshots is developed. Results suggest that the proposed algorithm offers the most relaxed statistical identifiability condition for multidimensional frequency estimation from finite snapshots.

In this paper, we derive the eigenfunctions of the Fourier transform (FT), the fractional FT (FRFT), and the linear canonical transform (LCT) with (1) complex parameters and (2) complex offsets. The eigenfunctions in the cases where the parameters and offsets are real were derived in literature. We extend the previous works to the cases of complex parameters and complex offsets. We first derive the eigenvectors of the offset discrete FT. They approximate the samples of the eigenfunctions of the continuous offset FT. We find that the eigenfunctions of the offset FT with complex offsets are the smoothed Hermite-Gaussian functions with shifting and modulation. Then we extend the results for the case of the offset FRFT and the offset LCT. We can use the derived eigenfunctions to simulate the self-imaging phenomenon for the optical system with energy-absorbing component, mode selection, encryption, and define the fractional Z-transform and the fractional Laplace transform. Index Terms--Eigenvalue, eigenvector, fractional Fourier transform (FRFT), fractional Laplace transform, fractional Z-transform, linear canonical transform (LCT), offset discrete FT (DFT).

For many clustering algorithms, such as K-Means, EM, and CLOPE, there is usually a requirement to set some parameters. Often, these parameters directly or indirectly control the number of clusters, that is, k, to return. In the presence of different data characteristics and analysis contexts, it is often difficult for the user to estimate the number of clusters in the data set. This is especially true in text collections such as Web documents, images, or biological data. In an effort to improve the effectiveness of clustering, we seek the answer to a fundamental question: How can we effectively estimate the number of clusters in a given data set? We propose an efficient method based on spectra analysis of eigenvalues (not eigenvectors) of the data set as the solution to the above. We first present the relationship between a data set and its underlying spectra with theoretical and experimental results. We then show how our method is capable of suggesting a range of k that is well suited to different analysis contexts. Finally, we conclude with further empirical results to show how the answer to this fundamental question enhances the clustering process for large text collections. Index Terms--Clustering, spectral methods, eigenvalues, eigenvectors.

An algorithm for computing the eigenvalue decomposition of a para-Hermitian polynomial matrix is described and the application to signal processing in terms of strong decorrelation and multichannel data compaction is brought out.

A dynamic antenna scheduling strategy for downlink MIMO communications is developed, where a subset of the receive antennas at certain users is selectively disabled. The results have shown that increasing the number of antennas at some users can degrade the signal-to-leakage-plus-noise (SLNR) performance at other users.

A nonparametric method is proposed for estimating the number of signals without eigendecomposition (MENSE) for the coherent narrowband signals impinging on a uniform linear array (ULA). The results have shown that MENSE is superior in detecting closely spaced signals with a small number of snapshots and at relatively low signal-to-noise ratio (SNR).

We propose a method for blind identification of multiple-input mutiple-out (MIMO) finite-impulse response (FIR) channels that exploits cyclostationarity of the received data induced at the transmitters by periodic precoding. It is shown that, by properly choosing the precoding sequence, the MIMO FIR transfer functions, with [M.sub.t] inputs and [M.sub.r] outputs, can be identified up to a unitary matrix ambiguity. The transfer functions need not be irreducible or column reduced, and there can be more outputs ([M.sub.r] [greater than or equal to] [M.sub.t]) or more inputs ([M.sub.r] < [M.sub.t]). The method exploits the linear relation between the covariance matrix of the received data and the 'channel product matrices'. The method is shown to be robust with respect to channel-order overestimation. The proposed algorithm requires solving linear equations and computing the nonzero eigenvalues and eigenvectors of a Hermitian positive semidefinite matrix. The performance of the algorithm, and indeed the identifiability, depends on the choice of the precoding sequence. We propose a method for optimal selection of the precoding sequence which takes into account the effect of additive channel noise and numerical error in covariance matrix estimation. Simulation results are used to demonstrate the performance of the algorithm. Index Terms--Blind identification, multiple-input mutiple-out (MIMO) channel, periodic precoding, transmitter induced cyclostationarity.

An equivalent resonant cavity model is proposed and developed for efficiently and accurately extracting the complex propagation constant of any arbitrary bounded and unbounded periodic guided-wave structures, which is known as a difficult eigenvalue problem with respect to a deterministic or S-parameter-based field solver. In this study, this problem is formulated as a standard eigenvalue one, which is made possible by effectively translating the transmission distance-related attenuation part of complex propagation constant into a time-dependent damping factor. This allows the development of an equivalent resonant cavity model to substitute or replace the periodic guided-wave model, leading to a complex frequency simulation model. As a result, the simulation time and storage requirement are then reduced significantly with this complex frequency approach. A finite-difference frequency-domain algorithm combined with this model is used to demonstrate the concept, and the properties of arbitrary complex closed/open periodic guided-wave structures are rigorously investigated. The proposed algorithm has been validated by both simulations and experiments. Index Terms--Equivalent resonant cavity model, finite-difference frequency-domain (FDFD) algorithm, large-scale standard eigenvalue problem, periodic guided-wave structure.

An improved whitening scheme for blind source separation, a novel biquadratic contrast function for extraction of independent sources and an efficient alternative method for joint implementation of a set of approximate diagonalization-structural matrices, is presented. The results have shown that the performance of the improved whitening scheme is much better than the classical whitening methods.

Much research has shown that the definitions of within-class and between-class scatter matrices and regularization technique are the key components to design a feature extraction for small sample size problems. In this paper, we illustrate the importance of another key component, eigenvalue decomposition method, and a new regularization technique was proposed. In the hyperspectral image experiment, the effects of these three components of feature extraction are explored on ill-posed and poorly posed conditions. The experimental results show that different regularization methods need to cooperate with different eigenvalue decomposition methods to reach the best performance, the proposed regularization method, regularized feature extraction (RFE) outperform others, and the best feature extraction for a small sample size classification problem is RFE with nonparametric weighted scatter matrices. Index Terms--Eigenvalue decomposition, feature extraction, genetic algorithm (GA), regularization, small sample size classification.

A procedure for the numerical calculation of photoacoustic signals is introduced. It is based on the finite element method and uses an expansion of the signal into acoustic eigenmodes of the measuring cell. Loss is included by the incorporation of quality factors. Surface and volume loss effects attributable to viscosity and thermal conductivity are considered. The method is verified for cylindrical cells with excellent accordance. The application to photoacoustic cells of unconventional shape yields good agreement with experimental data. OCIS codes: 120.6200, 000.4430.

Plunge milling operations are used to remove excess material rapidly in roughing operations. The cutter is fed in the direction of the spindle axis which has the highest structural rigidity. This paper presents a comprehensive model of plunge milling process by considering rigid body motion of the cutter, and three translational and torsional vibrations of the structure. The time domain simulation model allows prediction of cutting forces, torque, and vibrations while considering tool setting errors and time varying process parameters. The stability law is formulated as a four-dimensional eigenvalue problem, and the stability lobes are predicted directly with analytical solution in frequency domain. Time domain prediction of cutting forces and vibrations, as well as the frequency domain and chatter stability solution are verified with a series of plunge milling experiments. [DOI: 10.1115/1.2383070] Keywords: plunge milling, chatter, cutting force

A framework is described for identifying and estimating superimposed orientations. The eigensystem analysis has shown how to decompose the mixed-orientation parameters (MOPs) into individual orientations and also how to use tensor invariants to increase efficiency and derive a new feature for describing local neighborhoods which is invariant to rigid transformations.

This paper addresses real and reactive power management strategies of electronically interfaced distributed generation (DG) units in the context of a multiple-DG microgrid system. The emphasis is primarily on electronically interfaced DG (EI-DG) units. DG controls and power management strategies are based on locally measured signals without communications. Based on the reactive power controls adopted, three power management strategies are identified and investigated. These strategies are based on 1) voltage-droop characteristic, 2) voltage regulation, and 3) load reactive power compensation. The real power of each DG unit is controlled based on a frequency-droop characteristic and a complimentary frequency restoration strategy. A systematic approach to develop a small-signal dynamic model of a multiple-DG microgrid, including real and reactive power management strategies, is also presented. The microgrid eigen structure, based on the developed model, is used to 1) investigate the microgrid dynamic behavior, 2) select control parameters of DG units, and 3) incorporate power management strategies in the DG controllers. The model is also used to investigate sensitivity of the design to changes of parameters and operating point and to optimize performance of the microgrid system. The results are used to discuss applications of the proposed power management strategies under various microgrid operating conditions. Index Terms--Distributed generation (DG), droop characteristics, eigen analysis, microgrid, power management, real and reactive power control, small-signal dynamic analysis.

The goal of the optimal power flow (OPF) problem is to find an electric power system operating point that optimizes some objective. This optimization problem is constrained, however, since the operating point is constrained by Kirchhoff's laws and key operating limits. In this paper, we include small-signal stability limits in the OPF, which ensure that when small disturbances occur within the system, oscillations that occur in state variables such as generator rotor speed will decay quickly, returning the system to a normal operating point. We also account for security by using an objective function that is the expected value of social welfare. This objective function includes security costs such as generator ramping and load interruption that may be necessary when a contingency occurs. Software was written in Matlab to solve this optimization problem with small-signal stability constraints, and the software was used to find the optimal pre-contingency and post-contingency operating points of a nine-bus system with three generators. Index Terms--Eigenvalue sensitivities, optimal power flow (OPF), power system security, preventive control, small-signal stability, social-welfare maximization.

This paper describes a new algorithm to compute the dominant poles of a high-order multiple-input multiple-output (MIMO) transfer function. The algorithm, called the Subspace Accelerated MIMO Dominant Pole Algorithm (SAMDP), is able to compute the full set of dominant poles efficiently. SAMDP can be used to produce good modal equivalents automatically. The general algorithm is robust, applicable to both square and nonsquare transfer function matrices, and can easily be tuned to suit different practical system needs. Index Terms--Dominant pole spectrum, large-scale systems, modal analysis, modal equivalents, model reduction, multivariable systems, poorly damped oscillations, power system dynamics, small-signal stability, sparse eigenanalysis, system poles, transfer function, transfer function residues.

Stabilities of surface-tension-driven convection in an open cylinder are investigated numerically. The cylinder is heated laterally through its sidewall and is cooled at free surface by radiation. A seeding crystal at constant temperature is in contact with the free surface. Axisymmetric base flow is solved using the high-order finite difference method. Three-dimensional perturbation is applied to the obtained base flow to determine the critical Marangoni numbers at which the axisymmetry is broken. The eigenvalue matrix equation is solved using linear fractional transformation with banded matrix structure taken into account. Critical Marangoni-Reynolds numbers are obtained at various boundary conditions. [DOI: 10.1115/1.2353278] Keywords: Marangoni flow, linear stability analysis, crystal growth

The paper presents a bilevel strategy for the efficient optimum design of composite stiffened panels using VICONOPT, a fast-running optimization package based on linear eigenvalue buckling theory, and embracing practical composite design rules. Panel level optimization finds a minimum weight cross-sectional geometry based on a substitution of equivalent orthotropic plates for laminated plates. Optimization at the laminate level finds stacking sequences satisfying laminate design rules. VICONOPT models are validated with ABAQUS finite element models, and with experimental compressive testing of two blade-stiffened panels. The buckling and posthuckling behavior of the two panels, with initial buckling in the stiffeners and skin, respectively, is investigated in a high load and high strain range. The bilevel strategy is evaluated by the design of a relatively short Z stiffened panel which has been manufactured and tested, and also by design of a long wing cover panel with combined loads. The weight saving from the wing cover panel is 13% compared with an existing datum design. This demonstrated that the strategy is efficient, reliable, and extendable into the long panel range. DOI: 10.2514/1.22206

This paper describes a general approach for incorporating the eigenvector normalization condition in the computation of eigenvector design sensitivities. Design sensitivities for the eigenproblem have received much attention over the past four decades, however, previous work has focused primarily on mass normalized eigenvectors alone. The approach presented here considers conservative symmetric systems with distinct eigenvalues and addresses both first- and second-order eigenvalue and eigenvector design sensitivities. A rigorous treatment of the eigenvector normalization condition is provided by using its design derivative to eliminate the singularity issue in the eigenvector design sensitivity system of equations. The effect of rescaling eigenvectors is also considered, as is the related computational effort. Examples illustrate the computational procedure, and it is shown that the widely used Nelson's method is a special case of our more general approach. DOI: 10.2514/1.18760

A study poses and solves the analogue of Slepian's time-frequency concentration problem on the surface of the unit sphere to determine an orthogonal family of strictly bandlimited functions that are optimally concentrated within a closed region of the sphere or, alternatively, of strictly spacelimited functions that are optimally concentrated in the spherical harmonic domain. Results show that when the spatiospectral concentration region is an axisymmetric polar cap, the spatiospectral projection operator commutes with a Sturm-Liouville operator, which enables the eigenfunctions to be computed extremely accurately and efficiently, even when their area-bandwidth product, or Shannon number, is large.

For a q-parameter polynomial m x n matrix F of rank [rho], solutions of the equation Fx = 0 at points of the spectrum of the matrix F determined by [...]

An elementary proof of a formula for the 2-norm distance from a normal matrix A to the set of matrices with a multiple zero eigenvalue is given. Earlier, the authors [...]

According to a result of Wigner and von Neumann, the dimension of the set M of n x n real symmetric matrices with multiple eigenvalues is equal to N - [...]

The convergence of Feng's minor-component analysis (MCA) learning algorithm is studied through a corresponding deterministic discrete-time (DDT) system. Sufficient convergence conditions are obtained for Feng's MCA learning algorithm with constant learning rate.

We present a family of eigenvalue inequalities for the product of a Hermitian matrix and a positive-semidefinite matrix. Our theorem contains or extends some existing results on trace and eigenvalues. Index Term--Eigenvalue, inequality, singular value, trace.

A method to calculate the derivatives of the eigenvalues and eigenvectors of multiple-degree-of-freedom damped linear dynamic systems with respect to arbitrary design parameters is presented. In contrast to the traditional viscous damping model, a more general nonviscous damping model is considered. The nonviscous damping model is such that the damping forces depend on the past history of velocities via convolution integrals over given kernel functions. Because of the general nature of the damping, eigensolutions are generally complex valued, and eigenvectors do not satisfy the classical orthogonality relationship. The proposed method to calculate the eigenvector derivative depends only on the eigenvector concerned. Numerical examples are provided to illustrate the derived results.

We evaluate the eigenfields of an unstable Bessel--Gauss resonator (UBGR) by use of the transfer-matrix method in which the transverse profiles and their corresponding losses of the UBGR are considered as the eigenvectors and eigenvalues of a transfer matrix so that the dominant mode fields and their losses of the UBGR can be readily extracted in terms of the matrix eigenvalue algorithm. Moreover, based on the eigenfields across two mirrors that resulted from the transfer-matrix method, we simulate the field distributions in the cavity and the propagation of output beams by means of the angular spectrum method. The computation results show that the UBGR easily produces a fundamental Bessel--Gauss mode of good quality, and the output beams retain the original Bessel--Gauss distribution during propagation. OCIS codes: 140.3300, 140.3410, 140.4780.

This brief presents a new application of the theory of noise in free running oscillators based on the Floquet eigenvector decomposition. In oscillators, all orbital deviations contribute to the power density spectrum (PDS) as much as the 'phase' term, usually considered. Each orbital deviation component shows a time evolution depending on the related Floquet eigenvalue, which thus characterizes statistical properties related to that component. Orbital deviations are partially correlated, due to their common origin from noise sources, thus also correlation terms are considered in the evaluation of the PDS. In this brief, we introduce a simplified method of calculation of PDS and apply it to an example of RLC negative resistance oscillator. Results show the relevance of orbital deviations in PDS in presence of stationary noise, these contributions becomes particularly relevant when noise is cyclostationary. Index Terms--Floquet eigenvector decomposition, orbital deviation, oscillator noise, oscillators.

In this brief, a simple approach is proposed for decentralized control of linear large-scale systems. Sufficient conditions for diagonal dominance of closed-loop large-scale systems are derived. Based on these conditions, the interactions between the subsystems can be considered as external disturbances for each isolated subsystem. Then, a previously proposed approach is used to attenuate disturbances via dynamic output compensators based on complete parametric eigenstructure assignment. Through attenuation of the disturbances, the closed-loop poles of the overall system are assigned in the desirable region, by assigning the eigenstructure of each isolated subsystem appropriately. An example is given to show the effectiveness of the proposed method. Index Terms--Decentralized control, diagonal dominance, disturbance attenuation, eigenstructure assignment.