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At least 181 records · Page 10

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NASA NTRS1977

Separating and turbulent boundary layer calculations using polynomial interpretation

Higher order numerical methods derived from polynomial spline interpolation or Hermitian differencing are applied to a separating laminar boundary layer, i.e., the Howarth problem, and the turbulent flat plate boundary layer flow. Preliminary results are presented. It is found that accuracy equal to that of conventional second order accurate finite difference methods is achieved with many fewer mesh points and with reduced computer storage and time requirements.

Rubin, S. G.↗

NASA NTRS1977

On the equivalence of polynomial GCD and squarefree factorization problems

It is shown that a closer reexamination of Yun's 1976 paper reveals the reducibility of SQFR to GCD. The natural question that follows is whether GCD is reducible to SQFR. That is answered affirmatively and the derivation actually suggests an algorithm for computing GCD's when input polynomials are already represented by their SQFR form.

Yun, D. Y. Y.↗

NASA NTRS1977

Least squares polynomial fits and their accuracy

Equations are presented which attempt to fit least squares polynomials to tables of date. It is concluded that much data are needed to reduce the measurement error standard deviation by a significant amount, however at certain points great accuracy is attained.

Lear, W. M.↗

NASA NTRS1976

A computer program to find the kernel of a polynomial operator

This paper presents a FORTRAN program written to solve for the kernel of a matrix of polynomials with real coefficients. It is an implementation of Sain's free modular algorithm for solving the minimal design problem of linear multivariable systems. The structure of the program is discussed, together with some features as they relate to questions of implementing the above method. An example of the use of the program to solve a design problem is included.

Gejji, R. R.↗

NASA NTRS1977

Experimental evaluation of the tensor polynomial criterion for designing composite structures

A comprehensive experimental and analytical evaluation of the tensor polynomial failure criterion was undertaken to determine its capability for predicting the ultimate strength of a composite limina subject to a plane stress state. Results are presented demonstrating that a quadratic formulation is too conservative and a cubic representation is required. Strength comparisons with test data derived from glass/epoxy and graphite/epoxy tubular specimens are also provided to validate the cubic strength criterion. Environmental effects including ambient temperature, exposure to vacuum, length of post-cure time, and rate of cool down were also investigated. Behavior changes associated with polymer (epoxy) matrix composites were determined in terms of variations in stiffness and tensile strength.

Tennyson, R. C.↗

NASA NTRS1978

An efficient algorithm for choosing the degree of a polynomial to approximate discrete nonoscillatory data

An efficient algorithm for selecting the degree of a polynomial that defines a curve that best approximates a data set was presented. This algorithm was applied to both oscillatory and nonoscillatory data without loss of generality.

Hedgley, D. R.↗

NASA NTRS1977

Application of polynomial techniques to multivariable control of jet engines

This paper describes a complete case study of the application of the theory of minimal design to multivariable control of jet engines. The minimal-design problem is approached from the viewpoint of polynomial modules, and computational experience with PL/I and FORMAC-PL/I software is discussed. The complete minimal-design solution exhibits flexibilities not apparent in early industry studies, and a matrix approach to pole assignment can be used to advantage in this situation.

Gejji, R. R.↗

NASA NTRS1978

Evaluation of the tensor polynomial failure criterion for composite materials

Tennyson, R. C.↗

NASA NTRS1979

Astronomical applications of grazing incidence telescopes with polynomial surfaces

The report has examined the claim that grazing incidence telescopes having surfaces described by generalized equations have image characteristics superior to those of the paraboloid-hyperboloid and Wolter-Schwarzschild configurations. With emphasis on specific applications in solar and cosmic X-ray/EUV astronomy, raytracing has shown that in many cases there is no advantage in the polynomial design, and in those cases where advantages are theoretically to be expected, the advantages are outweighed by practical considerations.

Cash, W.↗

NASA NTRS1980

Polynomial approximation of functions in Sobolev spaces

Constructive proofs and several generalizations of approximation results of J. H. Bramble and S. R. Hilbert are presented. Using an averaged Taylor series, we represent a function as a polynomial plus a remainder. The remainder can be manipulated in many ways to give different types of bounds. Approximation of functions in fractional order Sobolev spaces is treated as well as the usual integer order spaces and several nonstandard Sobolev-like spaces.

Dupont, T.↗

NASA NTRS1980

Polynomial striction algorithms in the detection and determination of the characteristics of non-stationary phenomena

The effectiveness of the algorithm of polynomial striction of the data is examined, and the selection of an algorithm is carried out, according to the results of measurements of the components of the permanent magnetic field in communication sequences from the Venera-9 space vehicle, where the shock waves were recorded. It is shown that the most effective algorithm, according to the coefficient of striction, is the algorithm of the zero order interpolator. Also examined is the increase in effectiveness with the introduction of a variable threshold of comparison. The root-mean-square deviation of the error of regeneration of the data with various thresholds is calculated, and qualitative analysis of the distortions is carried out, having shown a considerable change in the form of the small discontinuities, which may be interpreted as potential interplanetary shock waves.

Yevdokimov, V. P.↗

NASA NTRS1980

Application of the cubic polynomial strength criterion to the failure analysis of composite materials

A comparative failure analysis is presented based on the application of quadratic and cubic forms of the tensor polynomial lamina strength criterion to various composite structural configurations in a plane stress state. Failure loads have been predicted for off-angle laminates under simple loading conditions and for symmetric-balanced laminates subject to varying degrees of biaxial tension, including configurations subject to multimode failures. Some experimental data are also provided to support these calculations. From these results, the necessity of employing a cubic strength criterion to accurately predict the failure of composite laminae is demonstrated.

Tennyson, R. C.↗

NASA NTRS1981

Fast polynomial transform and its implementation by computer

A fast polynomial transform (FPT) algorithm for computing two-dimensional cyclic convolutions on a general-purpose computer is demonstrated and compared with the FFT approach. An FPT program for two-dimensional convolutions written in FORTRAN is shown to be 20% faster than the conventional FFT algorithm. This higher speed advantage makes the FPT algorithm a candidate for many two-dimensional digital image filtering applications.

Reed, I. S.↗

NASA NTRS1981

Digital SAR processing using a fast polynomial transform

A new digital processing algorithm based on the fast polynomial transform is developed for producing images from Synthetic Aperture Radar data. This algorithm enables the computation of the two dimensional cyclic correlation of the raw echo data with the impulse response of a point target, thereby reducing distortions inherent in one dimensional transforms. This SAR processing technique was evaluated on a general-purpose computer and an actual Seasat SAR image was produced. However, regular production runs will require a dedicated facility. It is expected that such a new SAR processing algorithm could provide the basis for a real-time SAR correlator implementation in the Deep Space Network.

Butman, S.↗

NASA NTRS1980

Design of a recursive vector processor using polynomial splines

The problem of obtaining smoothed estimates of function values, particularly their derivatives, from a finite set of inaccurate measurements is considered. A recursive two-dimensional vector processor is introduced as an approximation to the nonrecursive constrained least-squares estimation. Here, piecewise bicubic Hermite polynomials are extensively used as approximating functions, and the smoothing integral is converted to a discrete quadratic form. This makes it possible to convert the problem of fitting an approximating function to one of estimating the function values and derivatives at the nodes.

Kim, C. S.↗

NASA NTRS1982

The optimization of convergence for Chebyshev polynomial methods in an unbounded domain

Grosch and Orszag (1977) have performed a numerical analysis of the problem of solving differential equations in a semiinfinite or infinite domain using Chebyshev polynomials. The principal limitation of the conducted study was that it was entirely empirical. Various differential equations were solved in different ways and the numbers were compared. The present investigation has the objective to extend the studies conducted by Grosch and Orszag by deriving asymptotic approximations to the Chebyshev coefficients of simple model functions. This approach makes it possible to conduct more systematic comparisons of different methods, extend the range of comparisons, and, perhaps most important, give simple analytic formulas for choosing the optimum domain size or mapping parameter L for various situations.

Boyd, J. P.↗

NASA NTRS1983

Convergence and stability properties of minimal polynomial and reduced rank extrapolation algorithms

The minimal polynomial and reduced rank extrapolation algorithms are two acceleration of convergence methods for sequences of vectors. In a recent survey these methods were tested and compared with the scalar, vector, topological epsilon algorithms, and were observed to be more efficient than the latter. It was also observed that the two methods have similar convergence properties. The convergence and stability properties of these methods are analyzed and the performance of the acceleration methods when applied to a class of vector sequences that includes those sequences obtained from systems of linear equations by using matrix iterative methods is discussed.

Sidi, A.↗

NASA NTRS1983

Polynomial driven time base and PN generator

In support of the planetary radar upgrade new hardware was designed to increase resolution and take advantage of new technology. Included is a description of the Polynomial Driven Time Base and PN Generator which is used for range gate coding in the planetary radar system.

Brokl, S. S.↗