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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 235 records · Page 13

Roots of polynomials by ratio of successive derivatives

An order of magnitude study of the ratios of successive polynomial derivatives yields information about the number of roots at an approached root point and the approximate location of a root point from a nearby point. The location approximation improves as a root is approached, so a powerful convergence procedure becomes available. These principles are developed into a computer program which finds the roots of polynomials with real number coefficients.

Crouse, J. E.↗

The computation of optimal control programmes using a modified successive sweep method.

A second-order method for numerically solving control optimization problems has been developed. The method, referred to as the modified sweep method (MSM), differs from the successive sweep method (SSM) proposed by McReynolds and Bryson (1965) in that the conditions for local control optimality are used to determine the control as an explicit function of the state variables and time. The control is eliminated from the problem and the solution to the resulting two-point boundary value problem can be obtained by linear perturbation methods. The modified sweep method proposed here uncouples the perturbation equations for the state variables and the Lagrange multipliers by using a generalized matrix-Riccati transformation of variables. The resulting algorithm for the numerical iteration process is concerned with determining the initial values of a set of Lagrange multipliers rather than correcting a numerical control programme over the entire time interval of interest.

Colunga, D.↗

Computer program to determine roots of polynomials by ratio of successive derivatives

High speed computing finds roots of polynomials with real number coefficients. Ratios of successive polynomial derivatives approach provides accurate roots-of-polynomial computer programs with very high reliability. With derivative ratio method, root analysis can still be done even though the polynomial and its lower order derivatives cannot be evaluated with sufficient accuracy.

Crouse, J. E.↗

A successive overrelaxation iterative technique for an adaptive equalizer

An adaptive strategy for the equalization of pulse-amplitude-modulated signals in the presence of intersymbol interference and additive noise is reported. The successive overrelaxation iterative technique is used as the algorithm for the iterative adjustment of the equalizer coefficents during a training period for the minimization of the mean square error. With 2-cyclic and nonnegative Jacobi matrices substantial improvement is demonstrated in the rate of convergence over the commonly used gradient techniques. The Jacobi theorems are also extended to nonpositive Jacobi matrices. Numerical examples strongly indicate that the improvements obtained for the special cases are possible for general channel characteristics. The technique is analytically demonstrated to decrease the mean square error at each iteration for a large range of parameter values for light or moderate intersymbol interference and for small intervals for general channels. Analytically, convergence of the relaxation algorithm was proven in a noisy environment and the coefficient variance was demonstrated to be bounded.

Kosovych, O. S.↗

Change in land use in the Phoenix (1:250,000) Quadrangle, Arizona between 1970 and 1972: Successful use of proposed land use classification system

Changes in land use in the Phoenix (1:250,000 scale) Quadrangle in Arizona have been mapped using only the images from ERTS-1, tending to verify the utility of a land use classification system proposed for use with ERTS images. The period of change investigated was from November 1970 to late summer or early fall, 1972. Seasonal changes also were studied using successive ERTS images. Types of equipment used to aid interpretation included a color additive viewer, a twenty-power magnifier, a density slicer, and a diazo copy machine for making ERTS color composites in hard copy. Types of changes detected have been: (1) cropland or rangeland developed for new residential areas; (2) rangeland converted to new cropland; and (3) possibly new areas of industrial or commercial development. A map of land use previously compiled from air photos was updated in this manner.

Place, J. L.↗

Flowfield analysis for successive oblique shock wave interactions with a turbulent boundary layer

A computation procedure is described for predicting flow fields which develop when successive interactions between oblique shock waves and a turbulent boundary layer occur. Computations were carried out for axisymmetric internal flows at free stream Mach numbers = 3.82 and 2.82. The effect of boundary layer bleed was considered for the free stream Mach number = 2.82 flow. A control volume analysis is used to predict changes in the flow field across the interactions. Two bleed flow models were considered. A turbulent boundary layer program was used to compute changes in the boundary layer between the interactions. The results given are for flows with two shock wave interactions and for bleed at the second interaction site. In principle the method described may be extended to account for additional interactions. The predicted results are compared with measured results and are shown to be in good agreement when the bleed flow rate is low (on the order of 3 percent of the boundary layer mass flow), or when there is no bleed. As the bleed flow rate is increased, differences between the predicted and measured results become larger. Shortcomings of the bleed flow models at higher bleed flow rates are discussed.

Sun, C. C.↗