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An iterative perturbation solution of the inverse potential problem
Atomic model potentials for spectroscopic and scattering data, using perturbation theory
Nonlinear generalizations of matrix diagonal dominance with application to Gauss-Seidel iterations.
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Iterative explicit guidance for low thrust spacecraft.
A retargeting procedure is developed for use as a nonlinear low thrust guidance scheme. The selection of a control program composed of a sequence of inertially fixed thrust-acceleration vectors permits all trajectory computations to be made with closed form expressions, and allows the controls to be represented by constant parameters, thrust-acceleration vectors and thrusting times. By requiring each trajectory to be time optimal, the guidance problem is transformed into a parameter optimization problem which is solved by the conjugate gradient method. The scheme is applied to a low thrust capture mission, and the results of computer simulations are presented.
A two-dimensional, iterative solution for the jet flap
A solution is presented for the jet-flapped wing in two dimensions. The main flow is assumed to be inviscid and incompressible. The flow inside the jet is considered irrotational and the upper and lower boundaries between the jet and free stream are assumed to behave as vortex sheets which allow no mixing. The solution is found to be in satisfactory agreement with two dimensional experimental results and other theoretical work for intermediate values of momentum coefficient, but the regions of agreement vary with jet exit angle. At small values of momentum coefficient, the trajectory for the jet, as computed by this method, has more penetration than that of other available data, while at high values of moment coefficient this solution results in less penetration of the jet into the main flow.
An Iterative Approach to the Feature Selection Problem
The problem dealt with concerns feature selection or reducing the dimension of the data to be processed from n to k. By reducing the dimension of the data from n to k, classification time is generally reduced. Yet the dimension reduction should not be so great that classification accuracy is impaired. Thus, the general problem is considered of classifying an n-dimensional observation vector x into one of m-distinct classes where each class is normally distributed with mean and covariance. It is shown that the probability of misclassification is minimized if a maximum likelihood classification procedure is used to classify the data. The dimension of each observation vector to be processed is conveniently reduced by performing the transformation y = Bx, where B is a K by n matrix of rank k. Thus, the n-dimensional classification problem transforms into a k-dimensional classification problem.
Variational solution to the radiative equation by the use of a step function. II - Extension to nonlinear case by iteration method.
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An analytical iterative algorithm for the prediction of special satellite orbit points with the Brouwer orbit theory.
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An iterative approach to the feature selection problem
The B-average divergence for m-distinct classes, resulting from the linear transformation y = Bx, is proposed as a feature selection criterion, where B is a k by n matrix of rank k not greater than n. It is shown that if the B-average divergence resulting from B is large enough, then the probability of misclassification, considered as a function f the class of all k by n matrices, is essentially minimized by B. A computer program, utilizing a gradient procedure, is developed to numerically maximize the B-average divergence and results are presented for the Cl flight line. For this example, corresponding to 9-distinct classes, most of the discriminatory information is found to lie in a 3-dimensional subspace, defined by an appropriately chosen 3 by 12 matrix B.
Iterative techniques to estimate signature vectors for mixture processing of multispectral data
Two methods for obtaining the required spectral signatures for a particular mixture model are considered. For the model considered, the spectral signatures become signature vectors. The first method is based upon determination of the signature vectors in such a way that a measure of the inconsistency between the mixture model and the observed data is minimized. The second method is based upon determination of the signature vectors in such a way that the estimated mean percentage coverage of individual species matches apriori or ground truth estimates. The two methods proposed are applied to actual multispectral data in order to verify the concepts presented.
On a combined Sturm sequence and inverse iteration technique for eigenproblem solution of spinning structures
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An iterative scheme for determining sea surface temperatures, temperature profiles, and humidity profiles from satellite-measured infrared data
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Accelerated iteration schemes for transonic flow calculations using fast poisson solvers
The use of a fast elliptic solver in combination with relaxation is presented as an effective way to accelerate the convergence of transonic flow calculations, particularly when a marching scheme can be used to treat the supersonic zone in the relaxation process.
Theory and methods related to the singular-function expansion and Landweber's iteration for integral equations of the first kind
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Iterative techniques for the solution of large linear systems in computational aerodynamics
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A study of the effects of vertical resolution and measurement errors on an iteratively inverted temperature profile
A direct inversion method for inverting the temperature profile from satellite-measured radiation is discussed. The nth power of the weighting function in the integral radiative-transfer equation is used as the weight in the averaging process. The vertical resolution of the inverted temperature profile and the response of the inverted temperature profile to the measurement errors are examined in terms of n. It is found that for smaller values of n, the vertical resolution and the effect of measurement errors are reduced. When n = 0, both the vertical resolution and error effect are minimum. The temperature profile is adjusted by a constant; any structure different from the initial shape cannot be resolved. This is equivalent to the case where the entire atmosphere is treated as one layer with a fixed shape of temperature profile. When n approaches infinity, both the vertical resolution and error effect are maximum. This is equivalent to the case where the entire atmosphere is divided into m (the number of spectral channels) layers. Within each layer, the temperatures are adjusted by a constant, and any structure different from the initial shape cannot be resolved. Also, the shape of the final solution is closer to the initial profile if the value of n is smaller.
Discrete analog of an iterative method for inverse eigenvalue problems for Jacobi matrices
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Computer program documentation: ISOCLS iterative self-organizing clustering program, program C094
The author has identified the following significant results. This program implements an algorithm which, ideally, sorts a given set of multivariate data points into similar groups or clusters. The program is intended for use in the evaluation of multispectral scanner data; however, the algorithm could be used for other data types as well. The user may specify a set of initial estimated cluster means to begin the procedure, or he may begin with the assumption that all the data belongs to one cluster. The procedure is initiatized by assigning each data point to the nearest (in absolute distance) cluster mean. If no initial cluster means were input, all of the data is assigned to cluster 1. The means and standard deviations are calculated for each cluster.