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Results for “functional approximation”

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.

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At least 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
NASA NTRS1978

The determination of gravity anomalies from geoid heights using the inverse Stokes' formula, Fourier transforms, and least squares collocation

A numerical method for the determination of gravity anomalies from geoid heights is described using the inverse Stokes formula. This discrete form of the inverse Stokes formula applies a numerical integration over the azimuth and an integration over a cubic interpolatory spline function which approximates the step function obtained from the numerical integration. The main disadvantage of the procedure is the lack of a reliable error measure. The method was applied on geoid heights derived from GEOS-3 altimeter measurements in the calibration area of the GEOS-3 satellite.

Rummel, R.↗
NASA NTRS1983

Spline approximation of quantile functions

The study reported here explored the development and utility of a spline representation of the sample quantile function of a continuous probability distribution in providing a functional description of a random sample and a method of generating random variables. With a spline representation, the random samples are generated by transforming a sample of uniform random variables to the interval of interest. This is useful, for example, in simulation studies in which a random sample represents the only known information about the distribution. The spline formulation considered here consists of a linear combination of cubic basis splines (B-splines) fit in a least squares sense to the sample quantile function using equally spaced knots. The following discussion is presented in five parts. The first section highlights major results realized from the study. The second section further details the results obtained. The methodology used is described in the third section, followed by a brief discussion of previous research on quantile functions. Finally, the results of the study are evaluated.

Schiess, J. R.↗
NASA NTRS1990

Neural computation of arithmetic functions

An area of application of neural networks is considered. A neuron is modeled as a linear threshold gate, and the network architecture considered is the layered feedforward network. It is shown how common arithmetic functions such as multiplication and sorting can be efficiently computed in a shallow neural network. Some known results are improved by showing that the product of two n-bit numbers and sorting of n n-bit numbers can be computed by a polynomial-size neural network using only four and five unit delays, respectively. Moreover, the weights of each threshold element in the neural networks require O(log n)-bit (instead of n-bit) accuracy. These results can be extended to more complicated functions such as multiple products, division, rational functions, and approximation of analytic functions.

Siu, Kai-Yeung↗
NASA NTRS2004

Representation of Ice Geometry by Parametric Functions: Construction of Approximating NURBS Curves and Quantification of Ice Roughness--Year 1: Approximating NURBS Curves

Software was developed to construct approximating NURBS curves for iced airfoil geometries. Users specify a tolerance that determines the extent to which the approximating curve follows the rough ice. The user can therefore smooth the ice geometry in a controlled manner, thereby enabling the generation of grids suitable for numerical aerodynamic simulations. Ultimately, this ability to smooth the ice geometry will permit studies of the effects of smoothing upon the aerodynamics of iced airfoils. The software was applied to several different types of iced airfoil data collected in the Icing Research Tunnel at NASA Glenn Research Center, and in all cases was found to efficiently generate suitable approximating NURBS curves. This method is an improvement over the current "control point formulation" of Smaggice (v.1.2). In this report, we present the relevant theory of approximating NURBS curves and discuss typical results of the software.

Dill, Loren H.↗
NASA NTRS1975

Multidimensional stochastic approximation using locally contractive functions

A Robbins-Monro type multidimensional stochastic approximation algorithm which converges in mean square and with probability one to the fixed point of a locally contractive regression function is developed. The algorithm is applied to obtain maximum likelihood estimates of the parameters for a mixture of multivariate normal distributions.

Lawton, W. M.↗
NASA NTRS1980

The HD 200775/NGC 7023 complex - A question of reddening

The separation of the observed reddening of HD 200775 into intrinsic and interstellar components is rediscussed in the light of new surface-brightness data for NGC 7023, the reflection nebula surrounding HD 200775. Appropriate correction for the nebular contribution to reported ultraviolet flux measurements of HD 200775 leads to new values due to dust reddening: E(B-V) sub D = 0.44, and due to intrinsic reddening: E(B-V) sub I = 0.13-0.26. The newly derived extinction curve for HD 200775 is characterized by an abnormally weak interstellar 2200 A absorption feature, and the deduced nebular brightness in the far-ultraviolet is consistent either with dust in NGC 7023 having a relatively high albedo (a approximately equal to 0.6) and a nearly isotropic phase function (g approximately equal to 0.2), or with low albedo dust (a approximately equal to 0.3) with a forward-throwing phase function (g approximately equal to 0.6).

Witt, A. N.↗
NASA NTRS1967

Renormalized Born approximation.

Renormalizing approximate wave functions so that amplitude is correct by means of matrix, with applications to Born approximation

BORN APPROXIMATION↗
NASA NTRS1972

Nth-order flat approximation of the signum function by a polynomial

In the interval studied, the signum function, sgn x, was demonstrated to be uniquely approximated by an odd polynomial f sub n (x) of order 2n-1, for which the approximation is nth order flat with respect to the points (1,1) and (-1,-1). A theorem was proved which states that for even integers n or = 2, the approximating polynomial has a pair of nonzero real roots + or - x sub n such that the x sub n form a monotonically decreasing sequence which converges to the root of 2 as n approaches infinity. For odd n i, f sub n (x) represents a strictly increasing monotonic function for all real x. As n tends to infinity, f sub n (x) converges to sgn x uniformly in two interval ranges.

Hosenthien, H. H.↗
NASA NTRS1990

Piecewise linear approximation for hereditary control problems

This paper presents finite-dimensional approximations for linear retarded functional differential equations by use of discontinuous piecewise linear functions. The approximation scheme is applied to optimal control problems, when a quadratic cost integral must be minimized subject to the controlled retarded system. It is shown that the approximate optimal feedback operators converge to the true ones both in the case where the cost integral ranges over a finite time interval, as well as in the case where it ranges over an infinite time interval. The arguments in the last case rely on the fact that the piecewise linear approximations to stable systems are stable in a uniform sense.

Propst, Georg↗
NASA NTRS1974

Partition function for a two dimensional plasma in the random phase approximation

The partition function for a two-dimensional plasma is evaluated within the random phase approximation. The periodic boundary conditions are fully taken into account by including the periodic image interactions. In the guiding-center limit, the negative temperature threshold energy is evaluated, and a value different from previous calculations results. When an identical random phase evaluated, and a value different from previous calculations results. When an identical random phase evaluation is applied to the finite gyroradius plasma, the Salzberg-Prager-May equation of state is recovered.

Seyler, C. E., Jr.↗
NASA NTRS1997

Optimal Approximation of Quadratic Interval Functions

Measurements are never absolutely accurate, as a result, after each measurement, we do not get the exact value of the measured quantity; at best, we get an interval of its possible values, For dynamically changing quantities x, the additional problem is that we cannot measure them continuously; we can only measure them at certain discrete moments of time t(sub 1), t(sub 2), ... If we know that the value x(t(sub j)) at a moment t(sub j) of the last measurement was in the interval [x-(t(sub j)), x + (t(sub j))], and if we know the upper bound D on the rate with which x changes, then, for any given moment of time t, we can conclude that x(t) belongs to the interval [x-(t(sub j)) - D (t - t(sub j)), x + (t(sub j)) + D (t - t(sub j))]. This interval changes linearly with time, an is, therefore, called a linear interval function. When we process these intervals, we get an expression that is quadratic and higher order w.r.t. time t, Such "quadratic" intervals are difficult to process and therefore, it is necessary to approximate them by linear ones. In this paper, we describe an algorithm that gives the optimal approximation of quadratic interval functions by linear ones.

Koshelev, Misha↗
NASA NTRS1974

Partition function for a two-dimensional plasma in the random-phase approximation

The partition function for a two-dimensional plasma is evaluated within the random-phase approximation. The periodic boundary conditions are taken fully into account by including the periodic image interactions. In the guiding-center limit, the 'negative temperature' threshold energy is evaluated, and a value different from previous calculations results. When an identical random-phase evaluation is applied to the finite-gyroradius plasma, the Salzberg-Prager-May equation of state is recovered.

Seyler, C. E., Jr.↗