On the use of generalized inverses in function minimization
Minimization algorithms unified derivation, using Hessian matrix inverse
Tewarson, R. P.↗
SEARCH · Engineering Papers
Results for “Inverse”
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.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Population inversion of A. U. V. atomic line in recombining plasma nozzle flow
Arc heated plasma expansion through nozzle, observing population inversion of neutral carbon self-absorption UV atomic line
Bowen, S. W.↗
Inversion of spin-stabilized spacecraft by mass translation - Some practical aspects
Spin stabilized spacecraft inversion by mass translation with momentum vector fixed in inertial space, calculating control mass dynamics
Beachley, N. H.↗
Applications of generalized inverses to estimation in a dynamic system
Generalized matrix inverses application to estimation of state vector in dynamic control system, determining covariance matrix of estimator
Prochaska, B. J.↗
Flight instrument and telemetry response and its inversion
Mathematical models of rate gyros, servo accelerometers, pressure transducers, and telemetry systems were derived and their parameters were obtained from laboratory tests. Analog computer simulations were used extensively for verification of the validity for fast and large input signals. An optimal inversion method was derived to reconstruct input signals from noisy output signals and a computer program was prepared.
Weinberger, M. R.↗
Iterative computation of generalized inverses, with an application to CMG steering laws
A cubically convergent iterative method for computing the generalized inverse of an arbitrary M X N matrix A is developed and a FORTRAN subroutine by which the method was implemented for real matrices on a CDC 3200 is given, with a numerical example to illustrate accuracy. Application to a redundant single-gimbal CMG assembly steering law is discussed.
Steincamp, J. W.↗
Formation of OH through inverse predissociation.
The formation of OH by inverse predissociation from continuum levels to the v = 1, k = 1 vibrational level of a repulsive molecular state originating from an asymptotic atomic ground state is discussed. A rate constant of (1 to 3) x 10 to the minus twentieth power cu cm/sec is calculated for temperatures greater than 20 K. Predicted OH densities are found to be consistent with observations in dense heavily obscured clouds, but appear to be somewhat low for H I clouds.
Julienne, P. S.↗
Inversion problem for ion-atom differential elastic scattering.
The paper describes a practical application of Remler's (1971) method by which one constructs a set of phase shifts from high resolution measurements of the differential elastic scattering of protons by rare-gas atoms. These JWKB phase shifts are then formally inverted to determine the corresponding intermolecular potentials. The validity of the method is demonstrated by comparing an intermolecular potential obtained by direct inversion of experimental data with a fairly accurate calculation by Wolniewicz (1965).
Rich, W. G.↗
Applications of generalized inverses to estimation in dynamic systems.
Generalized matrix inverses are used to obtain an estimation procedure for estimation of the state vector of a dynamic system. This sequential procedure is studied analytically with respect to the choice of an arbitrary vector. The covariance matrix of the estimator is determined and compared to the optimal Kalman type procedure. A numerical example illustrates the procedure and compares it to the optimal one.
Prochaska, B. J.↗
The general linear inverse problem - Implication of surface waves and free oscillations for earth structure.
The discrete general linear inverse problem reduces to a set of m equations in n unknowns. There is generally no unique solution, but we can find k linear combinations of parameters for which restraints are determined. The parameter combinations are given by the eigenvectors of the coefficient matrix. The number k is determined by the ratio of the standard deviations of the observations to the allowable standard deviations in the resulting solution. Various linear combinations of the eigenvectors can be used to determine parameter resolution and information distribution among the observations. Thus we can determine where information comes from among the observations and exactly how it constraints the set of possible models. The application of such analyses to surface-wave and free-oscillation observations indicates that (1) phase, group, and amplitude observations for any particular mode provide basically the same type of information about the model; (2) observations of overtones can enhance the resolution considerably; and (3) the degree of resolution has generally been overestimated for many model determinations made from surface waves.
Wiggins, R. A.↗
Comparison of measured and theoretical inverse bremsstrahlung and photoionization absorption of infrared radiation in a H-He plasma.
The absorption coefficients of 1.15- and 3.39-micrometer radiation for a homogeneous H-He plasma have been measured in a temperature and electron density range where the major absorption mechanisms are electron-ion inverse bremsstrahlung and neutral-atom photoionization. Measurements were made behind both the incident and reflected shock waves in a driven tube by recording the laser intensity transmitted along the tube diameter as a function of time. The measured values compare well with those obtained from theoretical calculations for a gas in thermodynamic equilibrium.
Billman, K. W.↗
A general relaxation method for inverse solution of the full radiative transfer equation.
The relaxation method for the inverse solution of the full radiative transfer equation is generalized to solve for all atmospheric parameters which appear in the integrand as functions or functionals, without any a priori information related to the expected solution. The method is illustrated by examples in the earth's atmosphere for the determination of water vapor mixing ratio profiles from observations in the 6.3-micron band.
Chahine, M. T.↗
The inverse problem of the optimal regulator.
The inverse problem of the optimal regulator is considered for a general class of multi-input systems with integral-type performance indices. A new phase variable canonical form is shown to be convenient for this analysis. The advantage of the canonical form is to separate the state variables into subvectors of directly controlled, indirectly controlled, and uncontrollable components. Necessary and sufficient conditions for optimized performance indices are given. With the nonlinearities of the system restricted to functions of the directly controlled state variables, additional results are developed about the nonnegative property of optimized loss functions.
Yokoyama, R.↗
Dynamics of the inverse pinch.
Experiments are performed on the plasma produced in a large inverse pinch using argon with no applied magnetic fields or preheating. A direct observation is made of the precursor ionization which initially raises the electron temperature and electrical conductivity. Calculations show that most of the mass is entrained in the current sheet, but that less than complete sweeping occurs at the lower velocities. The shock which is embedded in the current sheet closely resembles an ordinary gasdynamic shock. Consideration of the shock jump condition derived from the induction equation is shown to determine the frequent inability of the shock to separate from the current sheet.
Weisbach, M. F.↗
Transfer of gaseous oxygen from high-pressure containers and the Joule-Thomson inversion
From the experiments performed in study, it was determined that oxygen transferred at ambient temperature and pressures up to 10,000 psig consistently dropped in temperature. All results therefore indicate that gaseous oxygen transferred at ambient temperature does not exhibit Joule-Thomson inversion below 10,000 psig.
Schumann, E. R.↗
Mathematics of Profile Inversion
One-dimensional and multi-dimensional inversion techniques for processing remote atmospheric and ionospheric sounding data
Colin, L.↗
Recent developments in the inversion by the method of relaxation
The relaxation method for inverse solution of the full radiative transfer equation is generalized to solve for all the atmospheric parameters that appear in the integrand as functions or functionals, without any a priori information about the expected solution. Illustrations are presented using the 7.5 micron CH4 band for determining temperature profiles in the Jovian atmosphere, and the 6.3 micron band for determining the water vapor mixing ratio in the earth's atmosphere.
Chahine, M. T.↗
Profile inversion in presence of ray bending
Inversion of radio occultation data for planetary atmospheres and ionospheres has been performed using the seismological Herglotz-Wiechert method, as adapted by Phinney and Anderson to the radio-occultation case. Profile reconstruction performed in computer simulated experiments with this approach have been compared with the ones obtained with the straight-ray Abel transform. For a thin atmosphere and ionosphere, like the ones encountered on Mars, microwave occultation data can be inverted accurately with both methods. For a dense ionosphere like the sun's corona, ray bending of microwaves is severe, and recovered refractivity by the Herglotz-Wiechert method provides significant improvement over the straight-ray Abel transform: the error reduces from more than 60% to less than 20% at a height of 60,000 km above the base of the corona.
Wallio, H. A.↗