A least square distance curve fitting technique
Least square distance curve fitting method
Howell, J. Q.↗
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FITLOS - A FORTRAN program for fitting low order polynomial splines by the method of least squares
FORTRAN 4 program /FITLOS/ for fitting low-order polynomial splines of two and three degrees by least squares method
Smith, P. J.↗
Performance characteristics of a single-engine fighter model fitted with an in-flight thrust reverser
wind tunnel performance characteristics of single-engine fighter model fitted with in-flight thrust reverser
Maiden, D. L.↗
Parametric fit to electron transport properties
Experimental data acquired over the past few years were gathered, and parametric fits made to these data. The following properties of electron transport were represented by simple functions of atomic number and energy: transmitted electron number, transmitted electron spectra, range, backscatter coefficient, angular distribution, energy deposition, bremsstrahlung intensity and energy spectra, and bremsstrahlung angular distribution and photon attenuation. The formulas cover the energy ranges of interest in space shielding problems (0.1 to 10.0 MeV). Procedures for using these formulas in practical situations are suggested.
Lonergan, J. A.↗
A curve-fitting technique for the determination of gain and saturation intensity in homogeneously-broadened gas lasers: Application to a waveguide CO2 laser
A least squares curve-fitting algorithm is derived which allows the simultaneous estimation of the small signal gain and the saturation intensity from an arbitrary number of data points relating power output to the incidence angle of an internal coupling plate. The method is used to study the dependence of the two parameters on tube pressure and discharge current in a waveguide CO2 laser having a 2 mm diameter capillary. It is found that, at pressures greater than 28 torr, rising CO2 temperature degrades the small signal gain at current levels as low as three milliamperes.
Degnan, J. J.↗
Computer user's manual for a generalized curve fit and plotting program
A FORTRAN coded program has been developed for generating plotted output graphs on 8-1/2 by 11-inch paper. The program is designed to be used by engineers, scientists, and non-programming personnel on any IBM 1130 system that includes a 1627 plotter. The program has been written to provide a fast and efficient method of displaying plotted data without having to generate any additions. Various output options are available to the program user for displaying data in four different types of formatted plots. These options include discrete linear, continuous, and histogram graphical outputs. The manual contains information about the use and operation of this program. A mathematical description of the least squares goodness of fit test is presented. A program listing is also included.
Schlagheck, R. A.↗
A Monte Carlo investigation of experimental data requirements for fitting polynomial functions
This report examines the extent to which sample size affects the accuracy of a low order polynomial approximation of an experimentally observed quantity and establishes a trend toward improvement in the accuracy of the approximation as a function of sample size. The task is made possible through a simulated analysis carried out by the Monte Carlo method, in which data are generated by using several transcendental or algebraic functions as models. Contaminated data of varying amounts are fitted to linear quadratic or cubic polynomials, and the behavior of the mean-squared error of the residual variance is determined as a function of sample size. Results indicate that the effect of the size of the sample is significant only for relatively small sample sizes and diminishes drastically for moderate and large amounts of experimental data.
Canavos, G. C.↗
Curvilinear bicubic spline fit interpolation scheme
Modification of the rectangular bicubic spline fit interpolation scheme so as to make it suitable for use with a polar grid pattern. In the proposed modified scheme the interpolation function is expressed in terms of the radial length and the arc length, and the shape of the patch, which is a wedge or a truncated wedge, is taken into account implicitly. Examples are presented in which the proposed interpolation scheme was used to reproduce the equations of a hemisphere.
Chi, C.↗
An empirical analysis of the quantitative effect of data when fitting quadratic and cubic polynomials
A study is made of the extent to which the size of the sample affects the accuracy of a quadratic or a cubic polynomial approximation of an experimentally observed quantity, and the trend with regard to improvement in the accuracy of the approximation as a function of sample size is established. The task is made possible through a simulated analysis carried out by the Monte Carlo method in which data are simulated by using several transcendental or algebraic functions as models. Contaminated data of varying amounts are fitted to either quadratic or cubic polynomials, and the behavior of the mean-squared error of the residual variance is determined as a function of sample size. Results indicate that the effect of the size of the sample is significant only for relatively small sizes and diminishes drastically for moderate and large amounts of experimental data.
Canavos, G. C.↗
Low-cost tool set for removing brazed fittings
Set includes crimping tool and pull tube. Crimping tool is modified vise-grip pliers which has special jaws designed to crimp fittings. Pull tube has single thread on each end. Tube can be used once on each end before discarding.
Giandomenico, A.↗
Method of Characteristics Calculations and Computer Code for Materials with Arbitrary Equations of State and Using Orthogonal Polynomial Least Square Surface Fits
A numerical scheme using the method of characteristics to calculate the flow properties and pressures behind decaying shock waves for materials under hypervelocity impact is developed. Time-consuming double interpolation subroutines are replaced by a technique based on orthogonal polynomial least square surface fits. Typical calculated results are given and compared with the double interpolation results. The complete computer program is included.
Chang, T. S.↗
The effects of correlation on goodness of fit
Autocorrelated normal random variates were generated via computer and the effects of various levels of correlation on goodness of fit problems were studied. The results are useful in determining the distribution or estimating the parameters of populations that correlate observations such as wind speeds and temperature. The model used to generate the autocorrelated data is an autoregressive process of order 1. The Kolmogorov-Smirnov and chi-square statistics are used in the analysis. It was observed in the simulation that high positive correlations tend to shift the sample mean away from the population mean and negative correlations tend to shift the sample mean towards the population mean. In many cases, it was observed that positive and negative correlations tend to decrease the standard deviation. However, since this did not occur in all cases, no definite conclusion can be made regarding the standard deviation. Since the autoregressive process is a linear transformation, it is not surprising that normality was preserved. However, a possible extension of this problem could be to generate non-normal data and observe how the distribution is affected by correlation. Another extension might utilize another model such as autoregressive of order k or a moving average process of order k.
Kitchens, L. J.↗
A computer program for fitting smooth surfaces to an aircraft configuration and other three dimensional geometries
A computer program that uses a three-dimensional geometric technique for fitting a smooth surface to the component parts of an aircraft configuration is presented. The resulting surface equations are useful in performing various kinds of calculations in which a three-dimensional mathematical description is necessary. Programs options may be used to compute information for three-view and orthographic projections of the configuration as well as cross-section plots at any orientation through the configuration. The aircraft geometry input section of the program may be easily replaced with a surface point description in a different form so that the program could be of use for any three-dimensional surface equations.
Craidon, C. B.↗
Lines, connectors, joints, and fittings
The structural reliability of lines, connectors, joints, and fittings used in liquid and gaseous O2 systems was examined. Overstress and high velocity flow of gaseous O2 as they affect system failure are also examined. Special attention was given to efforts to determine factors for designing a reliable O2 transport system for operation at all possible pressures.
Source record↗
Convergence acceleration and shock fitting for transonic aerodynamics computations
Two problems in computational fluid dynamics are studied in the context of transonic small-disturbance theory - namely, (1) how to speed up the convergence for currently available iterative procedures, and (2) how a shock-fitting method may be adapted to existing relaxation procedures with minimal alterations in computer programming and storage requirements. The paper contributes to a clarification of error analyses for sequence transformations based on the power method (including also the nonlinear transforms of Aitken, Shanks, and Wilkinson), and to developing a cyclic iterative procedure applying the transformations. Examples testing the procedure for a model Dirichlet problem and for a transonic airfoil problem show that savings in computer time by a factor of three to five are generally possible, depending on accuracy requirements and the particular iterative procedure used.-
Hafez, M. M.↗
The anatomy of floating shock fitting
The floating shock fitting technique is examined. Second-order difference formulas are developed for the computation of discontinuities. A procedure is developed to compute mesh points that are crossed by discontinuities. The technique is applied to the calculation of internal two-dimensional flows with arbitrary number of shock waves and contact surfaces. A new procedure, based on the coalescence of characteristics, is developed to detect the formation of shock waves. Results are presented to validate and demonstrate the versatility of the technique.
Salas, M. D.↗
Flexible fitting for fluid lines
Tube fitting, consisting of movable tubular section containing two spring pressure Teflon actuated low friction seals, two standard connectors, and two hexagonal retaining nuts, provides flexible joint that allows axial and rotational motion.
Barajas, S. L.↗
Soft seat A-N fitting for vacuum use
Commercially available fittings are modified to produce leaktight connections at low cost.
Szuhai, A. B.↗