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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 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Demonstration of the rodeo algorithm on a quantum computer

The rodeo algorithm is an efficient algorithm for eigenstate preparation and eigenvalue estimation for any observable on a quantum computer. This makes it a promising tool for studying the spectrum and structure of atomic nuclei as well as other fields of quantum many-body physics. The only requirement is that the initial state has sufficient overlap probability with the desired eigenstate. While it is exponentially faster than well-known algorithms such as phase estimation and adiabatic evolution for eigenstate preparation, it has yet to be implemented on an actual quantum device. In this work, we apply the rodeo algorithm to determine the energy levels of a random one-qubit Hamiltonian, resulting in a relative error of 0.08% using mid-circuit measurements on the IBM Q device Casablanca. This surpasses the accuracy of directly-prepared eigenvector expectation values using the same quantum device. We take advantage of the high-accuracy energy determination and use the Hellmann-Feynman theorem to compute eigenvector expectation values for a different random one-qubit observable. For the Hellmann-Feynman calculations, we find a relative error of 0.7%. Here, we conclude by discussing possible future applications of the rodeo algorithm for multi-qubit Hamiltonians.

algorithm↗
NASA NTRS1972

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.↗
NASA NTRS1972

SYMAT, COVAR: Test Procedures for Matrix Calculations

The FORTRAN subroutine SYMAT and related subroutines are described. In essence SYMAT is an iterative algorithm in which the problem of finding eigenvalues and eigenvectors of a real symmetric matrix is transformed into an equivalent problem of finding eigenvalues and eigenvectors of an infinite sequence of matrices of order two. A DEMO PROGRAM contains a subroutine COVAR which is used to compute the covariance matrix (denoted by A) of a data matrix (denoted by X). Since a covariance matrix is symmetric it can be analyzed by using subroutine SYMAT.

Morris, W. L.↗
NASA NTRS1974

Information content of IRIS spectra

Spectra from the satellite instrument IRIS (infra red interferometer spectrometer) were examined to find the number of independent variables needed to describe these broadband high spectral resolution data. The radiated power in the atmospheric window from 771 to 981/cm was the first parameter chosen for fitting observed spectra. At succeeding levels of analysis the residual variability (observed spectrum - best fit spectrum) in an ensemble of observations was partioned into spectral eigenvectors. The eigenvector describing the largest fraction of this variability was examined for a strong spectral signature; the power in the corresponding spectral band was then used as the next fitting parameter. The measured power in nine spectral intervals, when inserted in the spectral fitting functions, was adequate to describe most spectra to within the noise level of IRIS. Considerations of relative signal strength and scales of atmospheric variability suggest a combination sounder (multichannel-broad field of view) scanner (window channel-small field of view) as an efficient observing instrument.

Price, J. C.↗
NASA NTRS1974

Analytical and experimental investigation of a 1/8-scale dynamic model of the shuttle orbiter. Volume 1: Summary report

A 1/8-scale structural dynamics model of the space shuttle orbiter was analyzed using the NASA Structural Analysis System (NASTRAN). Comparison of the calculated eigenvalues with preliminary test data for the unrestrained condition indicate that the analytical model was consistently stiffer, being about 20% higher in the first mode. The eigenvectors show reasonably good agreement with test data. A series of analytical and experimental investigations undertaken to resolve the discrepancy are described. Modifications in the NASTRAN model based upon these investigations resulted in close agreement for both eigenvalues and eigenvectors.

Mason, P. W.↗
NASA NTRS1975

Numerical techniques for the linear, nonadiabatic stellar pulsation problem

The linear, nonadiabatic eigenvalue problem is formulated using Castor's method for calculating radial pulsations of stellar models. Both left and right eigenvectors are calculated. Initial eigenvalues for the linear, nonadiabatic solutions are obtained from the adiabatic eigenvalues and left and right eigenvectors. The orthogonality relation is obtained. Simple formulas for the Newton method are given. The iteration procedure is constrained to improve convergence. The Newton method is less satisfactory than the secant method for difficult cases. The linear, nonadiabatic solutions are shown to be sensitive to the number of zones with tau smaller than 2/3, and the value of (P/P sub r) surface or tau (surface). Optimum values can be determined for the number of zones and tau (surface). Application of the method to Population II Cepheids is briefly presented.

Bednarek, T. A.↗
NASA NTRS1975

Information content in Iris spectra

Spectra from the satellite instrument Iris (infrared interferometer spectrometer) were examined to find the number of independent variables needed to describe the broad-band high-resolution spectral data. The radiated power in the atmospheric window from 771 to 981 per cm was the first parameter chosen for fitting observed spectra. At succeeding levels of analysis, the residual variability (observed spectrum minus best-fit spectrum) in an ensemble of observations was partitioned into spectral eigenvectors. The eigenvector describing the largest fraction of this variability was examined for a strong spectral signature; the power in the corresponding spectral band was then used as the next fitting parameter. The measured power in nine spectral intervals, when it was inserted in the spectral-fitting functions, was adequate to describe most spectra to within the noise level of Iris. Considerations of relative signal strength and scales of atmospheric variability suggest a combination sounder (multichannel, broad field of view) scanner (window channel, small field of view) as an efficient observing instrument.

Price, J. C.↗
NASA NTRS1977

Characteristic vector analysis as a technique for signature extraction of remote ocean color data

Characteristic vector analysis is being used to extract spectral signatures of suspended matter in the ocean from remote ocean color data collected with MOCS (Multichannel Ocean Color Sensor), a multispectral scanner. Spectral signatures appear to be obtainable either directly from characteristic vectors or through a transformation of these eigenvectors. Quantification of the suspended matter associated with each resulting signature seems feasible using associated coefficients generated by the technique. This paper presents eigenvectors associated with algae, 'sediment', acid waste, sewage sludge, and oil. The results suggest an efficient method of transmitting from satellites multispectral data of pollution in our oceans.

Grew, G. W.↗
NASA NTRS1979

On adaptive modal control of large flexible spacecraft

A recently developed strategy for adaptive sampled-data control of distributed parameter systems based on a plant modal expansion description and modal simultaneous identification and regulation algorithms is presented with frequent reference to the annular momentum control device (AMCD) test example. The requirements of observation spillover reduction and modal eigenvector shape prespecification, which are especially crucial to the proposed adaptive control strategy, are addressed. Individual low pass time filtering of sensed AMCD particle displacements is proposed for observation spillover reduction. A layered scheme incorporating 'eigenvector' shape improvement is outlined to combat the expansion basis prespecification requirement.

Johnson, C. R., Jr.↗
NASA NTRS1980

Research on the application of a decoupling algorithm for structure analysis

The mathematical theory for decoupling mth-order matrix differential equations is presented. It is shown that the decoupling precedure can be developed from the algebraic theory of matrix polynomials. The role of eigenprojectors and latent projectors in the decoupling process is discussed and the mathematical relationships between eigenvalues, eigenvectors, latent roots, and latent vectors are developed. It is shown that the eigenvectors of the companion form of a matrix contains the latent vectors as a subset. The spectral decomposition of a matrix and the application to differential equations is given.

Denman, E. D.↗
NASA NTRS1980

Preliminary demonstration of a robust controller design method

Alternative computational procedures for obtaining a feedback control law which yields a control signal based on measurable quantitites are evaluated. The three methods evaluated are: (1) the standard linear quadratic regulator design model; (2) minimization of the norm of the feedback matrix, k via nonlinear programming subject to the constraint that the closed loop eigenvalues be in a specified domain in the complex plane; and (3) maximize the angles between the closed loop eigenvectors in combination with minimizing the norm of K also via the constrained nonlinear programming. The third or robust design method was chosen to yield a closed loop system whose eigenvalues are insensitive to small changes in the A and B matrices. The relationship between orthogonality of closed loop eigenvectors and the sensitivity of closed loop eigenvalues is described. Computer programs are described.

Anderson, L. R.↗
NASA NTRS1981

Multilevel techniques for nonelliptic problems

Multigrid and multilevel methods are extended to the solution of nonelliptic problems. A framework for analyzing these methods is established. A simple nonelliptic problem is given, and it is shown how a multilevel technique can be used for its solution. Emphasis is on smoothness properties of eigenvectors and attention is drawn to the possibility of conditioning the eigensystem so that eigenvectors have the desired smoothness properties.

Jespersen, D. C.↗
NASA NTRS1983

Population Control of Self-Replicating Systems: Option C

From the conception and development of the theory of self-replicating automata by John von Neumann, others have expanded on his theories. In 1980, Georg von Tiesenhausen and Wesley A. Darbro developed a report which is a "first' in presenting the theories in a conceptualized engineering setting. In that report several options involving self-replicating systems are presented. One of the options allows each primary to generate n replicas, one in each sequential time frame after its own generation. Each replica is limited to a maximum of m ancestors. This study involves determining the state vector of the replicas in an efficient manner. The problem is cast in matrix notation, where F = fij is a non-diagonalizable matrix. Any element fij represents the number of elements of type j = (c,d) in time frame k+1 generated from type i = (a,b) in time frame k. It is then shown that the state vector is: bar F(k)=bar F (non-zero) X F sub K = bar F (non-zero) xmx J sub kx m sub-1 where J is a matrix in Jordan form having the same eigenvalues as F. M is a matrix composed of the eigenvectors and the generalized eigenvectors of F.

Mccord, R. L.↗
NASA NTRS1984

Universal single level implicit algorithm for gasdynamics

A single level effectively explicit implicit algorithm for gasdynamics is presented. The method meets all the requirements for unconditionally stable global iteration over flows with mixed supersonic and supersonic zones including blunt body flow and boundary layer flows with strong interaction and streamwise separation. For hyperbolic (supersonic flow) regions the method is automatically equivalent to contemporary space marching methods. For elliptic (subsonic flow) regions, rapid convergence is facilitated by alternating direction solution sweeps which bring both sets of eigenvectors and the influence of both boundaries of a coordinate line equally into play. Point by point updating of the data with local iteration on the solution procedure at each spatial step as the sweeps progress not only renders the method single level in storage but, also, improves nonlinear accuracy to accelerate convergence by an order of magnitude over related two level linearized implicit methods. The method derives robust stability from the combination of an eigenvector split upwind difference method (CSCM) with diagonally dominant ADI(DDADI) approximate factorization and computed characteristic boundary approximations.

Lombard, C. K.↗
NASA NTRS1983

Feature selection methodologies using simulated Thematic Mapper data

The present investigation is concerned with the determination of the intrinsic dimensionality of a simulated Thematic Mapper data set. In addition, the effectiveness and sensitivity of 'standard' statistics separability measures (i.e., transformed divergence) is evaluated in comparison to eigenvectors for identifying the optimum subset of the original Thematic Mapper Simulator (TMS) bands for classifying the various cover types. TMS data were collected on May 2, 1979 by NASA's NS001 aircraft multispectral scanner over a bottomland forested area in South Carolina near the city of Camden. It is found that the eigenvectors and eigenvalues of a covariance matrix from a multispectral scanner system (MSS) data set can be obtained without having to actually transform the data.

Dean, M. E.↗
NASA NTRS1986

Investigation of seasonal variability of the wind stress curl over the North Atlantic Ocean by means of empirical orthogonal function analysis

The seasonal variability of the wind stress curl over the North Atlantic is investigated by means of empirical orthogonal function (EOF) analysis. The curl field is calculated from 1 year of First Global GARP Experiment wind data. It was found that 44 percent of the variability is contained in four significant eigenvectors. Their spatial patterns are characterized by basin-sized oscillations with larger amplitude to the north of 40 deg N. Their associated time series coefficients have the highest amplitude during the winter and show a tendency toward a white frequency spectrum which nevertheless exhibits noticeable peaks or gaps at certain frequencies. Physically, the first EOF is seen as the seasonal fluctuations of the mean wind stress curl pattern. Five other eigenvectors are also found to be above the noise level, but they account for only a smaller percentage of variability (19 percent). They are characterized by smaller spatial scales than the basin size. Their time series coefficients show a whiter frequency spectrum.

Barnier, B.↗
NASA NTRS1986

A comparison of several methods for the calculation of vibration mode shape derivatives

Four methods for the calculation of derivatives of vibration mode shapes (eigenvectors) with respect to design parameters are reviewed and compared. These methods (finite difference method, Nelson's method, modal method and a modified modal method) are implemented in a general-purpose commercial finite element program and applied to a cantilever beam and a stiffened cylinder with a cutout. A beam tip mass, a beam root height and specific dimensions of the cylinder model comprise the design variables. Data are presented showing the amount of central processor time used to compute the first four eigenvector derivatives for each example problem; errors and rapidity of convergence of the approximate derivative to the exact derivative are taken into account. Nelson's method proved to be most reliable and efficient.

Sutter, T. R.↗
NASA NTRS1986

The use of multidate multichannel radiance data in urban feature analysis

Two images were obtained from thematic mappers on Landsats 4 and 5 over the Washington, DC area during November 1982 and March 1984. Selected training areas containing different types of urban land use were examined,one area consisting entirely of forest. Mean digital radiance values for each bandpass in each image were examined, and variances, standard deviations, and covariances between bandpasses were calculated. It has been found that two bandpasses caused forested areas to stand out from other land use types, especially for the November 1982 image. In order to evaluate quantitatively the possible utility of the principal components analysis in selected feature extraction, the eigenvectors were evaluated for principal axes rotations which rendered each selected land use type most separable from all other land use types. The evaluated eigenvectors were plotted as a function of land use type, whose order was decided by considering anticipated shadow component and by examining the relative loadings indicative of vegetation for each of the principal components for the different features considered. The analysis was performed for each seven-band image separately and for the two combined images. It was found that by combining the two images, more dramatic land use type separation could be obtained.

Duggin, M. J.↗