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At least 145 records · Page 8

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NASA NTRS1973

Nonlinear least squares - An aid to thermal property determination.

Nonlinear least squares techniques can be used to determine effective thermal conductivity values from experimental data. Comparisons between measured and predicted conductivity values indicate that the analytically determined values can be used with confidence in performing thermal protection system analyses. A study was performed to compare the relative efficiencies of different minimizing techniques; the method of Peckham was the most efficient.

Curry, D. M.↗

NASA NTRS1974

Least squares adjustment with relatively large observation errors, inaccurate initial approximations, or both

Least squares adjustment problems are considered in which the condition equations are nonlinear in both the observations and the adjustment parameters ('unknowns'). A solution algorithm is presented which takes into account the second (as well as the first) order derivatives in the adjustment residuals (observation errors) and the corrections to the initially available approximations to the adjustment parameters. The inclusion of second-order terms in the adjustment residuals is necessary whenever the adjustment residuals themselves cannot be regarded as negligible as compared to the adjustment parameters, i.e., whenever the linearized condition equations would no longer be practically equivalent to the rigorous ones. The consideration of second-order terms in the parameter corrections is completely independent of the second-order terms in the adjustment residuals.

Eichhorn, H.↗

NASA NTRS1974

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.↗

NASA NTRS1975

An initial feasibility stage for Stoer's constrained least squares algorithm

A procedure is described for computing an initial feasible vector, x sub 0, for Stoer's algorithm for solving the linear least squares problem subject to linear equality and inequality constraints. The procedure described fits well with Stoer's algorithm since much of the computation performed to determine x sub 0 accomplishes initializing transformations of the problem data, which would otherwise be done in Stoer's algorithm after being given an x sub 0.

Lawson, C. L.↗

NASA NTRS1975

Sequential Least-Squares Using Orthogonal Transformations

Square root information estimation, starting from its beginnings in least-squares parameter estimation, is considered. Special attention is devoted to discussions of sensitivity and perturbation matrices, computed solutions and their formal statistics, consider-parameters and consider-covariances, and the effects of a priori statistics. The constant-parameter model is extended to include time-varying parameters and process noise, and the error analysis capabilities are generalized. Efficient and elegant smoothing results are obtained as easy consequences of the filter formulation. The value of the techniques is demonstrated by the navigation results that were obtained for the Mariner Venus-Mercury (Mariner 10) multiple-planetary space probe and for the Viking Mars space mission.

Bierman, G. J.↗

NASA NTRS1975

A least mean squares CUBIC algorithm for on-line differential of sampled analog signals

A digital computer algorithm is developed for on-line time differentiation of sampled analog voltage signals. The derivative is obtained by employing a least mean squares technique. The recursive algorithm results in a considerable reduction in computer time compared to a complete new solution of the normal equations each time a new data point is accepted. Implementation of the algorithm on a digital computer is discussed. Examples are simulated on a DEC PDP-8 computer.

Allum, J. H. J.↗

NASA NTRS1975

Fixed memory least squares filtering

Buxbaum has reported on three algorithms for computing least squares estimates that are based on fixed amounts of data. In this correspondence, the filter is arranged as a point-deleting Kalman filter concatenated with the standard point-inclusion Kalman filter. The resulting algorithm is couched in a square root framework for greater numerical stability, and special attention is given to computer implementation.

Bierman, G. J.↗

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 NTRS1977

The incomplete inverse and its applications to the linear least squares problem

A modified matrix product is explained, and it is shown that this product defiles a group whose inverse is called the incomplete inverse. It was proven that the incomplete inverse of an augmented normal matrix includes all the quantities associated with the least squares solution. An answer is provided to the problem that occurs when the data residuals are too large and when insufficient data to justify augmenting the model are available.

Morduch, G. E.↗

NASA NTRS1976

A method for the selection of a functional form for a thermodynamic equation of state using weighted linear least squares stepwise regression

A method was developed for establishing a rational choice of the terms to be included in an equation of state with a large number of adjustable coefficients. The methods presented were developed for use in the determination of an equation of state for oxygen and nitrogen. However, a general application of the methods is possible in studies involving the determination of an optimum polynomial equation for fitting a large number of data points. The data considered in the least squares problem are experimental thermodynamic pressure-density-temperature data. Attention is given to a description of stepwise multiple regression and the use of stepwise regression in the determination of an equation of state for oxygen and nitrogen.

Jacobsen, R. T.↗

NASA NTRS1979

Concerning an application of the method of least squares with a variable weight matrix

An estimate of a state vector for a physical system when the weight matrix in the method of least squares is a function of this vector is considered. An iterative procedure is proposed for calculating the desired estimate. Conditions for the existence and uniqueness of the limit of this procedure are obtained, and a domain is found which contains the limit estimate. A second method for calculating the desired estimate which reduces to the solution of a system of algebraic equations is proposed. The question of applying Newton's method of tangents to solving the given system of algebraic equations is considered and conditions for the convergence of the modified Newton's method are obtained. Certain properties of the estimate obtained are presented together with an example.

Sukhanov, A. A.↗

NASA NTRS1978

The case for at least three mare basalt magmas at the Luna 24 landing site

Petrographic and electron microprobe studies have been carried out for 1230 particles from the Luna 24 drill core. At least three mare basalts were distinguished on the basis of major and minor element chemical compositions of pyroxenes. Mg-rich monomineralic particles of olivine and pyroxene defined one major type. The other two magmas were identified by the Ti/(Ti + Cr) ratio at constant Fe/(Fe + Mg) ratio in pyroxenes derived from polymineralic igneous lithic fragments. Whole rock chemical analyses for V and Cr also provided evidence for these distinct magmas.

Nielsen, R. L.↗

NASA NTRS1979

On the Routh approximation technique and least squares errors

A new method for calculating the coefficients of the numerator polynomial of the direct Routh approximation method (DRAM) using the least square error criterion is formulated. The necessary conditions have been obtained in terms of algebraic equations. The method is useful for low frequency as well as high frequency reduced-order models.

Aburdene, M. F.↗

NASA NTRS1980

Stratospheric NO2 and H2O mixing ratio profiles from high resolution infrared solar spectra using nonlinear least squares

Nonlinear least squares spectral curve fitting has been used to derive vertical mixing ratio profiles for NO2 and H2O above 16 km from high resolution (0.2/cm) solar spectra collected during sunset with a balloon borne interferometer. The NO2 profile shows a sharp peak of 8 ppbv at 32 km falling rapidly to less than 0.5 ppbv at 17 km. The H2O profile shows a broad peak of 6.5 ppmv at 30 km falling to less than 4 ppmv at 17 km.

Niple, E.↗

NASA NTRS1980

Statistically conditioned least squares retrievals planned for the VAS demonstration experiment

Problems in the retrieval of atmospheric profiles from passively observed satellite radiances are reviewed. Plans are described for statistically conditioned least squares retrievals of temperature and moisture profiles around mesoscale events, based upon the expected sensitivity of the VAS channels to the atmospheric variations. Simulated soundings for a global data set and for the 1976 National Storm Laboratory (NSSL) severe storm data set are also examined. This combination of radiance modeling and statistical conditioning should yield reliable mesoscale soundings and provide a test bed for sounding research and development with the VAS instrument.

Chester, D.↗

NASA NTRS1981

On the method of least squares. II

A least squares method proposed previously for solving a general class of problems is expanded in two ways. First, covariance matrices related to the solution are calculated and their interpretation is given. Second, improved methods of solving the normal equations related to those of Marquardt (1963) and Fletcher and Powell (1963) are developed for this approach. These methods may converge in cases where Newton's method diverges or converges slowly.

Jefferys, W. H.↗

NASA NTRS1984

Least-Squares Prediction of Solar Activity

Studies of statistical methods for predicting future solar activity described in report containing extensive graphical and tabular presentations of analyses. Lagrangian-least-squares method, which gives best predictions presented in detail. FORTRAN source code for method given.

Holland, R. L.↗

NASA NTRS1983

Elastomer coated filler and composites thereof comprising at least 60% by weight of a hydrated filler and an elastomer containing an acid substituent

The impact resistance of flame retardant composites, especially thermoplastic molding: compounds containing over 60% hydrated mineral filler such as Al(OH)3 or Mg(OH)2 as improved by coating the filler with 1 to 20% of an elastomer. The composite will fail by crazing or shearing rather than by brittle fracture. A well bonded elastomeric interphase resulted by utilizing acidic substituted resins such as ethyl-hexyl acrylate-acrylic acid copolymers which bond to and are cross-linked by the basic filler particles. Further improvement in impact resistance was provided by incorporating 1 to 10% of a resin fiber reinforcement such as polyvinyl alcohol fibers that decompose to yield at least 30% water when heated to decomposition temperature.

Mueller, W. A.↗