Search NASA⌕ Search

SEARCH · Search NASA

Results for “ITERATION”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 325 records · Page 18
All sourcesNASA NTRSDOE OSTI
NASA NTRS1972

Transient, compressible heat and mass transfer in porous media using the strongly implicit iteration procedure.

Coupled nonlinear partial differential equations describing heat and mass transfer in a porous matrix are solved in finite difference form with the aid of a new iterative technique (the strongly implicit procedure). Example numerical results demonstrate the characteristics of heat and mass transport in a porous matrix such as a charring ablator. It is emphasized that multidimensional flow must be considered when predicting the thermal response of a porous material subjected to nonuniform boundary conditions.

Curry, D. M.↗
NASA NTRS1972

Applications of partial orderings to the study of positive definiteness, monotonicity, and convergence of iterative methods for linear systems.

Most of the known results concerning convergence of iterative methods for solving linear systems involve either positive definiteness or monotonicity. In this paper a new concept, called K-semipositivity, is introduced, which provides a link between convergence theory, monotonicity, and positive definiteness. By using this concept, together with partial orderings in Euclidean n-space, several new convergence theorems are proved. Application to Jacobi's methods and the theory of regular splittings shows the usefulness of these new results.

Vandergraft, J. S.↗
NASA NTRS1972

Limb radiance inversion: Iterative convergence for a nonlinear kernal

The features of the limb inversion problem that differentiate it from the nadir problem are described; the most important of these are the sharply peaked weighting functions and the nonlinear kernel that arises because the atmosphere is required to be in hydrostatic balance. The problem may be split into two parts: given the pressure at one level and the measured radiances, can the temperatures be retrieved? And how can the pressure be obtained at one level? The second problem is shown to depend on the first, which is solved iteratively. The convergence properties and final accuracies are presented. Inversion to obtain trace constituents is briefly discussed.

Gille, J. C.↗
NASA NTRS1972

The solution of the relaxation problem for the Boltzmann equation by the integral iteration method

The Boltzmann equation is considered in terms of the problem of relaxation of some initial distribution function which depends only on velocities, to Maxwell's distribution function. The Boltzmann equation is given for the relaxation problem in which the distribution function f(t, u, v) is time dependent and is also dependent on two other variables u and v (the velocities of rigid spherical molecules). An iteration process is discussed in which the velocity space u, v is subdivided into squares, the distribution function in each square being approximated by the second-order surface from the values of the distribution function at nine points. The set of all of these points forms a network of u, v values at the nodes of which the distribution function can be found.

Limar, Y. F.↗
NASA NTRS1973

Rapid iterative reanalysis for automated design

A method for iterative reanalysis in automated structural design is presented for a finite-element analysis using the direct stiffness approach. A basic feature of the method is that the generalized stiffness and inertia matrices are expressed as functions of structural design parameters, and these generalized matrices are expanded in Taylor series about the initial design. Only the linear terms are retained in the expansions. The method is approximate because it uses static condensation, modal reduction, and the linear Taylor series expansions. The exact linear representation of the expansions of the generalized matrices is also described and a basis for the present method is established. Results of applications of the present method to the recalculation of the natural frequencies of two simple platelike structural models are presented and compared with results obtained by using a commonly applied analysis procedure used as a reference. In general, the results are in good agreement. A comparison of the computer times required for the use of the present method and the reference method indicated that the present method required substantially less time for reanalysis. Although the results presented are for relatively small-order problems, the present method will become more efficient relative to the reference method as the problem size increases. An extension of the present method to static reanalysis is described, ana a basis for unifying the static and dynamic reanalysis procedures is presented.

Bhatia, K. G.↗
NASA NTRS1973

Comments on 'An iterative clustering procedure.'

The limitation of the iterative clustering procedure proposed by Haralick and Dinstein is indicated with the help of two examples and is construed as the effect of the linear structure of the T transformation.

Kan, E. P. F.↗
NASA NTRS1973

Eigenproblem solution by a combined Sturm sequence and inverse iteration technique.

Description of an efficient and numerically stable algorithm, along with a complete listing of the associated computer program, developed for the accurate computation of specified roots and associated vectors of the eigenvalue problem Aq = lambda Bq with band symmetric A and B, B being also positive-definite. The desired roots are first isolated by the Sturm sequence procedure; then a special variant of the inverse iteration technique is applied for the individual determination of each root along with its vector. The algorithm fully exploits the banded form of relevant matrices, and the associated program written in FORTRAN V for the JPL UNIVAC 1108 computer proves to be most significantly economical in comparison to similar existing procedures. The program may be conveniently utilized for the efficient solution of practical engineering problems, involving free vibration and buckling analysis of structures. Results of such analyses are presented for representative structures.

Gupta, K. K.↗
NASA NTRS1974

An iterative technique to stabilize a linear time invariant multivariable system with output feedback

An iterative procedure for determining the constant gain matrix that will stabilize a linear constant multivariable system using output feedback is described. The use of this procedure avoids the transformation of variables which is required in other procedures. For the case in which the product of the output and input vector dimensions is greater than the number of states of the plant, general solution is given. In the case in which the states exceed the product of input and output vector dimensions, a least square solution which may not be stable in all cases is presented. The results are illustrated with examples.

Sankaran, V.↗
NASA NTRS1974

Iterative solution of transonic flows over airfoils and wings, including flows at Mach 1

A new method of calculating transonic flows based on a 'rotated' difference scheme is described. It is suitable for the calculation of both two- and three-dimensional flows without restriction on the speed at infinity and is well adapted to computer use. The Murman procedure is modified to eliminate any assumptions about the direction of flow when constructing the difference scheme. The proper directional property is obtained by rotating the difference scheme to conform with the local stream direction. In the hyperbolic region retarded difference formulas are used for all contributions to the streamwise second derivative, producing a correctly oriented positive artificial viscosity. In the absence of a simple implicit scheme in the hyperbolic and elliptic regions, the concept of iterations as steps in artificial time is introduced. Computer testing of this procedure provides numerical confirmation of the existence and uniqueness of weak solutions of the potential equation when a suitable entropy inequality is enforced.

Jameson, A.↗
NASA NTRS1974

A new adaptive classifier using iterative filtering

To cope with signature variability, an algorithm has been defined which will adaptively classify remotely sensed data in the visible and near infrared band. The signal is divided into a space-dependent component and a target-dependent component. The target-dependent component is assumed fixed across the image for each target type. The space-dependent component is estimated iteratively by a weighted, least-squares algorithm. Included are the derivations of the sensor model and the two-dimensional, estimation algorithm.

Actkinson, A. L.↗
NASA NTRS1975

Stepwise Iterative Fourier Transform: The SIFT

A program, designed specifically to study the respective effects of some common data problems on results obtained through stepwise iterative Fourier transformation of synthetic data with known waveform composition, was outlined. Included in this group were the problems of gaps in the data, different time-series lengths, periodic but nonsinusoidal waveforms, and noisy (low signal-to-noise) data. Results on sinusoidal data were also compared with results obtained on narrow band noise with similar characteristics. The findings showed that the analytic procedure under study can reliably reduce data in the nature of (1) sinusoids in noise, (2) asymmetric but periodic waves in noise, and (3) sinusoids in noise with substantial gaps in the data. The program was also able to analyze narrow-band noise well, but with increased interpretational problems. The procedure was shown to be a powerful technique for analysis of periodicities, in comparison with classical spectrum analysis techniques. However, informed use of the stepwise procedure nevertheless requires some background of knowledge concerning characteristics of the biological processes under study.

Benignus, V. A.↗
NASA NTRS1975

The determination of orbits using Picard iteration

The determination of orbits by using Picard iteration is reported. This is a direct extension of the classical method of Picard that has been used in finding approximate solutions of nonlinear differential equations for a variety of problems. The application of the Picard method of successive approximations to the initial value and the two point boundary value problems is given.

Mikkilineni, R. P.↗
NASA NTRS1975

An iterative procedure for obtaining maximum-likelihood estimates of the parameters for a mixture of normal distributions, Addendum

New results and insights concerning a previously published iterative procedure for obtaining maximum-likelihood estimates of the parameters for a mixture of normal distributions were discussed. It was shown that the procedure converges locally to the consistent maximum likelihood estimate as long as a specified parameter is bounded between two limits. Bound values were given to yield optimal local convergence.

Peters, B. C., Jr.↗
NASA NTRS1976

The Davidon-Fletcher-Powell penalty function method: A generalized iterative technique for solving parameter optimization problems

The Fletcher-Powell version of the Davidon variable metric unconstrained minimization technique is described. Equations that have been used successfully with the Davidon-Fletcher-Powell penalty function technique for solving constrained minimization problems and the advantages and disadvantages of using them are discussed. The experience gained in the behavior of the method while iterating is also related.

Johnson, I. L., Jr.↗
NASA NTRS1976

An iterative procedure for obtaining maximum-likelihood estimates of the parameters for a mixture of normal distributions, 2

The problem of obtaining numerically maximum likelihood estimates of the parameters for a mixture of normal distributions is addressed. In recent literature, a certain successive approximations procedure, based on the likelihood equations, is shown empirically to be effective in numerically approximating such maximum-likelihood estimates; however, the reliability of this procedure was not established theoretically. Here, a general iterative procedure is introduced, of the generalized steepest-ascent (deflected-gradient) type, which is just the procedure known in the literature when the step-size is taken to be 1. With probability 1 as the sample size grows large, it is shown that this procedure converges locally to the strongly consistent maximum-likelihood estimate whenever the step-size lies between 0 and 2. The step-size which yields optimal local convergence rates for large samples is determined in a sense by the separation of the component normal densities and is bounded below by a number between 1 and 2.

Peters, B. C., Jr.↗