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Hydrodynamic characteristics producing inward pumping in mechanical face seals, solving Reynolds equation for hydrodynamic lubrication with short-bearing approximation and numerical iterative methods
Iterative method for reducing filters required for optimal Kalman filter design maintaining parameter estimation accuracy
Iterative method for designing supersonic body of revolution from surface pressure distribution
Iterative method determining variation of any order of planned circular orbit about rotating gravitational source
Potential calculation from given source distribution, including direct and iterative methods, error analysis, convergence, computer programs and applications in plasma physics
Analysis of four iterative methods for approximating zeros of polynomial expressions using digital computer
An iterative method, which is characterized as a maximum-likelihood minimum-variance technique, was used to extract the aerodynamic parameters of a Navion airplane from flight data. The purposes were to compare the results with parameters obtained from wind-tunnel tests and with results obtained by analog matching the same data, and to develop techniques for application of the parameter extraction program. Results from the study showed that the parameter-extraction program can produce aerodynamic parameters which will permit close estimation of the aircraft time histories used in the extraction process. The program determined an estimate of the standard deviations of the states and parameters. These estimates were used to indicate how well the calculated states fit the flight data and the confidence in the values of the estimated parameters. The study also showed that the values of the parameters were affected by the data and mathematical model used during the extraction process. Because of the lack of confidence in the parameters extracted by use of some of the sets of data, several parameters were estimated by other methods. By using a combination of methods, a set of parameters which gave a fit to the data was obtained.
A cubically convergent iterative method for computing the generalized inverse of an arbitrary M X N matrix A is developed and a FORTRAN subroutine by which the method was implemented for real matrices on a CDC 3200 is given, with a numerical example to illustrate accuracy. Application to a redundant single-gimbal CMG assembly steering law is discussed.
Classical iterative methods in nonlinear regression are reviewed and improved upon. This is accomplished by discussion of the geometrical and theoretical motivation for introducing modifications using generalized matrix inversion. Examples having inherent pitfalls are presented and compared in terms of results obtained using classical and modified techniques. The modification is shown to be useful alone or in conjunction with other modifications appearing in the literature.
The structure of strong plane shock waves in a perfect monatomic gas was studied using four nonlinear models of the Boltzmann equation. The models involved the use of a simplified collision operator with velocity-independent collision frequency, in place of the complicated Boltzmann collision operator. The models employed were the BGK and ellipsoidal models developed by earlier authors, and the polynomial and trimodal gain function models developed during the work. An exact set of moment equations was derived for the density, velocity, temperature, viscous stress, and heat flux within the shock. This set was reduced to a pair of coupled nonlinear integral equations and solved using specially adapted numerical techniques. A new and simple Gauss-Seidel iteration was developed during the work and found to be as efficient as the best earlier iteration methods.
Using stiffness matrix and lumped-mass representation specified number of natural frequencies are obtained using inverse iteration method. Mode shapes for each frequency are also obtained. These frequencies and mode shapes can be found in reasonable periods of computer time utilizing this code.
The n-dimensional scattering problem is solved by means of a k-space formulation of the field equations, thereby replacing the conventional integral equation formulation by a set of two algebraic equations in two unknowns in two spaces (the constitutive equation being an algebraic equation in x-space). These equations are solved by an iterative method with the aid of the fast Fourier transform (FFT) algorithm connecting the two spaces, requiring very simple initial approximations. Since algebraic and FFT equations are used, the number of arithmetic multiple-add operations and storage allocations required for a numerical solution are reduced from the order of N sq (for solving the matrix equations resulting from the conventional integral equations) to the order of N(log base 2 of N) and N, respectively (where N is the number of data points required for the specification of the problem). The advantage gained in speed and storage is thus of the order of N/log base 2 of N and N, respectively. This method is thus considerably more efficient than the conventional matrix method, and permits exact numerical solutions for much larger problems. Arguments are presented toward the view that the field equations are more fundamental in k-space. The details and some numerical results of the application of this method to the three-dimensional electromagnetic scattering problems are presented as an example.
Classical iterative methods in nonlinear regression are reviewed and improved upon. This is accomplished by discussion of the geometrical and theoretical motivation for introducing modifications using generalized matrix inversion. Examples having inherent pitfalls are presented and compared in terms of results obtained using classical and modified techniques. The modification is shown to be useful alone or in conjunction with other modifications appearing in the literature.
Optimum airfoils in the sense of maximum lift coefficient are obtained for incompressible fluid flow at large Reynolds number. The maximum lift coefficient is achieved by requiring that the turbulent skin friction be zero in the pressure rise region on the airfoil upper surface. Under this constraint, the pressure distribution is optimized. The optimum pressure distribution is a function of Reynolds number and the trailing edge velocity. Geometries of those airfoils which will generate these optimum pressure distributions are obtained using a direct-iterative method which is developed in this study. This method can be used to design airfoils consisting of any number of elements. Numerical examples of one- and two-element airfoils are given. The maximum lift coefficients obtained range from 2 to 2.5.
Numerical solutions for radiative transport in a class of anisotropically scattering materials are presented. Conditions for convergence and divergence of the iterative method are given and supported by computed results. The relation of two flux theories to the equation of radiative transfer for isotropic scattering is discussed. The adequacy of the two flux approach for the reflectance, radiative flux and radiative flux divergence of highly scattering media is evaluated with respect to solutions of the radiative transfer equation.
Conditions of self-sustained oscillations in a two-axis model of the nonlinear LST system are studied. The describing function of the CMG frictional nonlinearity of the LST system is used for the analysis, as well as continuous-data and discrete-data models of the simplified LST control system. A numerical-iterative method is described for the analysis of the two-axis system. Approximation methods and the direct plotting of the stability equation are implemented in the study. It is shown that although the dynamics of the two axes are identical, the amplitudes of self-sustained oscillations in the two axes may in principle be different. Analysis shows that the LST systems are of equal amplitudes but with 180-degree phase shift.
Wozencraft and Kennedy have suggested that the appropriate demodulator criterion of goodness is the cut-off rate of the discrete memoryless channel created by the modulation system; the criterion of goodness adopted in this note is the symmetric cut-off rate which differs from the former criterion only in that the signals are assumed equally likely. Massey's necessary condition for optimal demodulation of binary signals is generalized to M-ary signals. It is shown that the optimal demodulator decision regions in likelihood space are bounded by hyperplanes. An iterative method is formulated for finding these optimal decision regions from an initial good quess. For additive white Gaussian noise, the corresponding optimal decision regions in signal space are bounded by hypersurfaces with hyperplane asymptotes; these asymptotes themselves bound the decision regions of a demodulator which, in several examples, is shown to be virtually optimal. In many cases, the necessary condition for demodulator optimality is also sufficient, but a counter example to its general sufficiency is given.
An iterative method to invert size distributions from simulated scattered radiance measurements at small angles from the sun has been investigated. The inferred size distributions were represented by piecewise linear and cubic spline functions. Various relevant characteristics were investigated and it was found that: (1) the inverted size distribution was insensitive to the number of knots in the piecewise linear spline; (2) within the range of sensitivity, the choice of initial guess had little effect on the inverted size distribution; (3) five per cent random noise in the simulated radiances appreciably deteriorated the result but variations are still tolerable when compared with other methods for determining size distributions; (4) the inverted distribution was insensitive to the index of refraction used in the kernel for particle radii greater than 1 micron; (5) the choice of wavelength between 0.40 and 0.70 microns has a negligible effect on the inverted distribution; (6) a range of tropospheric aerosol size distributions gives acceptable inverted results; and (7) the cubic spline representation can give reasonable inverted distributions, but may become unstable.