Search NASA⌕ Search

SEARCH · Search NASA

Results for “Inversion”

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.

At least 325 records · Page 18
All sourcesNASA NTRSDOE OSTI
NASA NTRS1974

Analysis of RAE-1 inversion

The RAE-1 spacecraft inversion performed October 31, 1972 is described based upon the in-orbit dynamical data in conjunction with results obtained from previously developed computer simulation models. The computer simulations used are predictive of the satellite dynamics, including boom flexing, and are applicable during boom deployment and retraction, inter-phase coast periods, and post-deployment operations. Attitude data, as well as boom tip data, were analyzed in order to obtain a detailed description of the dynamical behavior of the spacecraft during and after the inversion. Runs were made using the computer model and the results were analyzed and compared with the real time data. Close agreement between the actual recorded spacecraft attitude and the computer simulation results was obtained.

Hedland, D. A.↗
NASA NTRS1976

Recursive partitioned inversion of large (1500 x 1500) symmetric matrices

A recursive algorithm was designed to invert large, dense, symmetric, positive definite matrices using small amounts of computer core, i.e., a small fraction of the core needed to store the complete matrix. The described algorithm is a generalized Gaussian elimination technique. Other algorithms are also discussed for the Cholesky decomposition and step inversion techniques. The purpose of the inversion algorithm is to solve large linear systems of normal equations generated by working geodetic problems. The algorithm was incorporated into a computer program called SOLVE. In the past the SOLVE program has been used in obtaining solutions published as the Goddard earth models.

Putney, B. H.↗
NASA NTRS1976

Adequacy of classical inverse bremsstrahlung theory for low-temperature plasmas

The authors examine those plasma heating conditions under which a theory more accurate than the classical inverse bremsstrahlung theory should be used to predict absorption coefficients when laser energy is injected into the plasma. A correlation plot for measured absorption coefficients at three laser wavelengths versus those calculated by quantum mechanical theory yields a correlation coefficient for the least-squares fit of 0.994. A plot of the ratio of the quantum-mechanically corrected electron ion inverse bremsstrahlung absorption coefficient to that calculated by classical methods versus plasma temperature shows that at around 20 eV and above the differences between classical and quantum predictions are negligible, but significant errors could arise from application of classical theories to lower-temperature plasmas. Some recent experiments in the literature are shown to be worthy of reinterpretation in this light.

Billman, K. W.↗
NASA NTRS1976

The solar occultation technique for remote sensing of particulates in the earth's atmosphere. I - The inversion of horizon radiances from space

The aerosol scattering coefficient as a function of height can be recovered from a direct inversion of the single-scattering horizon radiance provided the sun is above the horizon and an independent measurement of extinction as a function of height is made. Aerosol detection is effected by means of spacecraft measurements of the horizon radiance made during periods of spacecraft twilight. A solar occultation technique which allows the twilight measurements to be made when the sun is still above the horizon greatly reduces the complexity of the inversion problem. The second part of the paper reports on the use of a coronograph aboard Skylab to photograph the horizon just before spacecraft twilight in order to monitor the aerosol component above the tropopause. The coronograph picture, centered on 26.5 degrees E longitude and 63.0 degrees S latitude, shows that the aerosol layer peaks at a height of 48 plus or minus 1 km.

Schuerman, D. W.↗
NASA NTRS1977

A method of inversion of satellite magnetic anomaly data

A method of finding a first approximation to a crustal magnetization distribution from inversion of satellite magnetic anomaly data is described. Magnetization is expressed as a Fourier Series in a segment of spherical shell. Input to this procedure is an equivalent source representation of the observed anomaly field. Instability of the inversion occurs when high frequency noise is present in the input data, or when the series is carried to an excessively high wave number. Preliminary results are given for the United States and adjacent areas.

Mayhew, M. A.↗
NASA NTRS1977

Experience with the inversion of Nimbus 4 BUV measurements to retrieve the ozone profile

The relative merits of pressure increment and partial derivative formulations of the ozone inversion problem are discussed briefly. The height range of validity of the retrieved ozone profile and the effects of adding wavelengths to or of dropping wave-length from the inversion system are indicated. Illustrative results are presented for profiles retrieved from BUV data using Backus-Gilbert, minimum information (Twomey), and quasi-optimum procedures.

Mateer, C. L.↗
NASA NTRS1978

Inverse boundary-layer theory and comparison with experiment

Inverse boundary layer computational procedures, which permit nonsingular solutions at separation and reattachment, are presented. In the first technique, which is for incompressible flow, the displacement thickness is prescribed; in the second technique, for compressible flow, a perturbation mass flow is the prescribed condition. The pressure is deduced implicitly along with the solution in each of these techniques. Laminar and turbulent computations, which are typical of separated flow, are presented and comparisons are made with experimental data. In both inverse procedures, finite difference techniques are used along with Newton iteration. The resulting procedure is no more complicated than conventional boundary layer computations. These separated boundary layer techniques appear to be well suited for complete viscous-inviscid interaction computations.

Carter, J. E.↗
NASA NTRS1978

Line shapes /absorption coefficients/ for satellites and inversion of the data to obtain interaction potentials

Line shapes for cesium broadened by xenon and neopentane have been measured in an absorption cell. The growth of the red satellites, both primary and secondary, were studied on the first five principal series doublets and on the first S-D forbidden doublet. An inversion scheme based on a nearest-neighbor density was employed to invert the measured line shapes and obtain difference potential estimates. It is apparent from the inversion scheme that minor inflections in the difference potential map into strong features in the frequency plane and that contrary to popular assumption, absolute extrema may not be necessary for satellite interpretation. Strength effects observed on the forbidden satellites also demonstrate that the radial dependence of the dipole moment must be accounted for in certain cases.

Exton, R. J.↗
NASA NTRS1978

The determination of gravity anomalies from geoid heights using the inverse Stokes' formula, Fourier transforms, and least squares collocation

A numerical method for the determination of gravity anomalies from geoid heights is described using the inverse Stokes formula. This discrete form of the inverse Stokes formula applies a numerical integration over the azimuth and an integration over a cubic interpolatory spline function which approximates the step function obtained from the numerical integration. The main disadvantage of the procedure is the lack of a reliable error measure. The method was applied on geoid heights derived from GEOS-3 altimeter measurements in the calibration area of the GEOS-3 satellite.

Rummel, R.↗
NASA NTRS1979

Numerical methods for problems involving the Drazin inverse

The objective was to try to develop a useful numerical algorithm for the Drazin inverse and to analyze the numerical aspects of the applications of the Drazin inverse relating to the study of homogeneous Markov chains and systems of linear differential equations with singular coefficient matrices. It is felt that all objectives were accomplished with a measurable degree of success.

Meyer, C. D., Jr.↗
NASA NTRS1979

Inverse boundary-layer technique for airfoil design

A description is presented of a technique for the optimization of airfoil pressure distributions using an interactive inverse boundary-layer program. This program allows the user to determine quickly a near-optimum subsonic pressure distribution which meets his requirements for lift, drag, and pitching moment at the desired flow conditions. The method employs an inverse turbulent boundary-layer scheme for definition of the turbulent recovery portion of the pressure distribution. Two levels of pressure-distribution architecture are used - a simple roof top for preliminary studies and a more complex four-region architecture for a more refined design. A technique is employed to avoid the specification of pressure distributions which result in unrealistic airfoils, that is, those with negative thickness. The program allows rapid evaluation of a designed pressure distribution off-design in Reynolds number, transition location, and angle of attack, and will compute an airfoil contour for the designed pressure distribution using linear theory.

Henderson, M. L.↗
NASA NTRS1979

Note on the practical significance of the Drazin inverse

The solution of the differential system Bx = Ax + f where A and B are n x n matrices, and A - Lambda B is not a singular pencil, may be expressed in terms of the Drazin inverse. It is shown that there is a simple reduced form for the pencil A - Lambda B which is adequate for the determination of the general solution and that although the Drazin inverse could be determined efficiently from this reduced form it is inadvisable to do so.

Wilkinson, J. H.↗
NASA NTRS1978

Aerosol size distributions obtained by inversion of spectral optical depth measurements

Columnar aerosol size distributions have been inferred by numerically inverting particulate optical depth measurements as a function of wavelength. An inversion formula which explicitly includes the magnitude of the measurement variances is derived and applied to optical depth measurements obtained in Tucson with a solar radiometer. It is found that the individual size distributions of the aerosol particles (assumed spherical), at least for radii greater than or approximately equal to 0.1 micron, fall into one of three distinctly different categories. Approximately 50% of all distributions examined thus far can best be represented as a composite of a Junge distribution plus a distribution of relatively monodispersed larger particles centered at a radius of about 0.5 micron. Scarcely 20% of the distributions yielded Junge size distributions, while 30% yielded relatively monodispersed distributions of the log-normal or gamma distribution types. A representative selection of each of these types will be presented and discussed. The sensitivity of spectral attenuation measurements to the radii limits and refractive index assumed in the numerical inversion will also be addressed.

King, M. D.↗
NASA NTRS1978

Stochastic inverse problem in the radiation of noise

The reported investigation is concerned with a stochastic inverse radiation problem in a uniform medium. The problem is illustrated with the aid of a simple model consisting of an array of point sources. The entropy functional is chosen to be the structural functional in determining the source distribution. A general theory for the stochastic inverse problem is introduced. It is shown that the general procedure yields the methods of the Lagrangian multiplier, when the structural and residual functionals are specialized. Tihonov's regularization and a method related to generalized or pseudoinverses are also obtained. Examples considered for purposes of illustration are related to a continuous source with the least noise intensity, a continuous source with a potential, and an axisymmetric line source.

Chow, P. L.↗
NASA NTRS1979

Inversion of satellite magnetic anomaly data

A method of finding a first approximation to a crustal magnetization distribution from inversion of satellite magnetic anomaly data is described. Magnetization is expressed as a Fourier series in a segment of spherical shell. Input to this procedure is an equivalent source representation of the observed anomaly field. Instability of the inversion occurs when high frequency noise is present in the input data, or when the series is carried to an excessively high wave number. Preliminary results are given for the United States and adjacent areas.

Mayhew, M. A.↗
NASA NTRS1979

A new inversion method of remote sounding of planetary atmospheres

A new inversion method for remote sounding of planetary atmospheres is presented which appears to have several significant advantages over the conventional methods. This method is applicable to high-resolution observations where the spectral lines are fully resolved and is based on matching the calculated slopes of the spectral line profiles with slopes of the observed line shapes. The method is applied to inversion of ozone absorption lines in the earth's atmosphere, and the results are compared with those obtained by a conventional method. The proposed method is seen to provide a significant improvement in the overall accuracy of the retrieved profiles, with higher vertical resolution and higher levels which may be probed.

Abbas, M. M.↗
NASA NTRS1979

Modular theory of inverse systems

The relationship between multivariable zeros and inverse systems was explored. A definition of zero module is given in such a way that it is basis independent. The existence of essential right and left inverses were established. The way in which the abstract zero module captured previous definitions of multivariable zeros is explained and examples are presented.

Source record↗
NASA NTRS1980

Inversion and approximation of Laplace transforms

A method of inverting Laplace transforms by using a set of orthonormal functions is reported. As a byproduct of the inversion, approximation of complicated Laplace transforms by a transform with a series of simple poles along the left half plane real axis is shown. The inversion and approximation process is simple enough to be put on a programmable hand calculator.

Lear, W. M.↗