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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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All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

Preconditioned domain decomposition scheme for three-dimensional aerodynamic sensitivity analysis

A discrete sensitivity analysis algorithm had previously been developed and applied to two-dimensional aerodynamic optimization problems, where the computational domains were discretized by using single grids. The sparse, unsymmetric systems of linear equations resulting from this algorithm were solved by a direct matrix inversion matrix. However, for large two-dimensional problems and, practically, all three-dimensional problems, direct inversion methods become inapplicable, primarily due to the prohibitive computer storage needed. In an attempt to alleviate such hindrances, the sensitivity analysis with domain decomposition (SADD) scheme was developed. This scheme divides the computational domain into smaller and nonoverlapping subdomains (multiblock grids) that are solved separately. Then, the final solution is constructed from the subdomain solutions. As the number of grid points in the interface boundaries of the subdomains becomes large, the computer memory required to store the effective coefficient matrix of these interface points starts to increase. Presented in this Technical Note is a preconditioned iterative procedure to overcome this particular problem.

Eleshaky, Mohamed E.↗
NASA NTRS1981

Iterative optical vector-matrix processors (survey of selected achievable operations)

An iterative optical vector-matrix multiplier with a microprocessor-controlled feedback loop capable of performing a wealth of diverse operations was described. A survey and description of many of its operations demonstrates the versatility and flexibility of this class of optical processor and its use in diverse applications. General operations described include: linear difference and differential equations, linear algebraic equations, matrix equations, matrix inversion, nonlinear matrix equations, deconvolution and eigenvalue and eigenvector computations. Engineering applications being addressed for these different operations and for the IOP are: adaptive phased-array radar, time-dependent system modeling, deconvolution and optimal control.

Casasent, D.↗
NASA NTRS1988

Fast polar decomposition of an arbitrary matrix

The polar decomposition of an m x n matrix A of full rank, where m is greater than or equal to n, can be computed using a quadratically convergent algorithm. The algorithm is based on a Newton iteration involving a matrix inverse. With the use of a preliminary complete orthogonal decomposition the algorithm can be extended to arbitrary A. How to use the algorithm to compute the positive semi-definite square root of a Hermitian positive semi-definite matrix is described. A hybrid algorithm which adaptively switches from the matrix inversion based iteration to a matrix multiplication based iteration due to Kovarik, and to Bjorck and Bowie is formulated. The decision when to switch is made using a condition estimator. This matrix multiplication rich algorithm is shown to be more efficient on machines for which matrix multiplication can be executed 1.5 times faster than matrix inversion.

Higham, Nicholas J.↗
NASA NTRS1989

An order (n) algorithm for the dynamics simulation of robotic systems

The formulation of an Order (n) algorithm for DISCOS (Dynamics Interaction Simulation of Controls and Structures), which is an industry-standard software package for simulation and analysis of flexible multibody systems is presented. For systems involving many bodies, the new Order (n) version of DISCOS is much faster than the current version. Results of the experimental validation of the dynamics software are also presented. The experiment is carried out on a seven-joint robot arm at NASA's Goddard Space Flight Center. The algorithm used in the current version of DISCOS requires the inverse of a matrix whose dimension is equal to the number of constraints in the system. Generally, the number of constraints in a system is roughly proportional to the number of bodies in the system, and matrix inversion requires O(p exp 3) operations, where p is the dimension of the matrix. The current version of DISCOS is therefore considered an Order (n exp 3) algorithm. In contrast, the Order (n) algorithm requires inversion of matrices which are small, and the number of matrices to be inverted increases only linearly with the number of bodies. The newly-developed Order (n) DISCOS is currently capable of handling chain and tree topologies as well as multiple closed loops. Continuing development will extend the capability of the software to deal with typical robotics applications such as put-and-place, multi-arm hand-off and surface sliding.

Chun, H. M.↗
NASA NTRS1973

HYMPS: Numerical Techniques

The digital calculations that drive the classification portion of the Hybrid Pattern Recognition System (HYMPS) are considered. A revision of these calculations is suggested that involves three items: matrix inversion, det calculations and singularity, and covariance factorization. It is shown that it is more economical to first factor the covariance matrix, and by so doing, delete the matrix inversion routine. In addition, the necessary det calculations can be more easily realized by use of simple theoretical facts about the factorization.

Decell, H. P., Jr.↗
NASA NTRS1986

Analysis of harmonic spline gravity models for Venus and Mars

Methodology utilizing harmonic splines for determining the true gravity field from Line-Of-Sight (LOS) acceleration data from planetary spacecraft missions was tested. As is well known, the LOS data incorporate errors in the zero reference level that appear to be inherent in the processing procedure used to obtain the LOS vectors. The proposed method offers a solution to this problem. The harmonic spline program was converted from the VAX 11/780 to the Ridge 32C computer. The problem with the matrix inversion routine that improved inversion of the data matrices used in the Optimum Estimate program for global Earth studies was solved. The problem of obtaining a successful matrix inversion for a single rev supplemented by data for the two adjacent revs still remains.

Bowin, Carl↗
NASA NTRS1989

Analysis of modified SMI method for adaptive array weight control

An adaptive array is applied to the problem of receiving a desired signal in the presence of weak interference signals which need to be suppressed. A modification, suggested by Gupta, of the sample matrix inversion (SMI) algorithm controls the array weights. In the modified SMI algorithm, interference suppression is increased by subtracting a fraction F of the noise power from the diagonal elements of the estimated covariance matrix. Given the true covariance matrix and the desired signal direction, the modified algorithm is shown to maximize a well-defined, intuitive output power ratio criterion. Expressions are derived for the expected value and variance of the array weights and output powers as a function of the fraction F and the number of snapshots used in the covariance matrix estimate. These expressions are compared with computer simulation and good agreement is found. A trade-off is found to exist between the desired level of interference suppression and the number of snapshots required in order to achieve that level with some certainty. The removal of noise eigenvectors from the covariance matrix inverse is also discussed with respect to this application. Finally, the type and severity of errors which occur in the covariance matrix estimate are characterized through simulation.

Dilsavor, R. L.↗
NASA NTRS1966

Matrix methods and automation in structural engineering

The partial differential equations of motion of shell structures subject to arbitrary loads may be extremely difficult or even impossible to solve. Since the digital computer is now an available tool for the structural engineer, current research has been directed toward methods which involve matrix formulation of large systems of algebraic equations and matrix solutions for discrete elements rather than the solution of the partial differential equations. These methods require rapid and accurate computer solutions. Recognizing the accuracy problems inherent in working with large matrices, a comprehensive survey of available computer programs was performed for large matrix inversion and for eigenvalue and eigenvector solutions under a Research Grant from the National Aeronautics and Space Administration and the techniques are developed in this paper for using these programs most efficiently for structural applications. The contents of the paper include: automation of matrix compilation, methods of very large matrix inversion and solution of simultaneous equation, and techniques for finding eigenvalues and vectors. In addition, a finite element stiffness matrix approach developed at the Denver Research Institute for both plates and shells subject to arbitrary dynamic loads is described as it was instrumented with complete automation on the digital computer.

Anita S West↗
NASA NTRS1981

Effects of multiple scattering and surface albedo on the photochemistry of the troposphere

The effect of treatment of incoming solar radiation on the photochemistry of the troposphere is discussed. A one dimensional photochemical model of the troposphere containing the species of the nitrogen, oxygen, carbon, hydrogen, and sulfur families was developed. The vertical flux is simulated by use of the parameterized eddy diffusion coefficients. The photochemical model is coupled to a radiative transfer model that calculates the radiation field due to the incoming solar radiation which initiates much of the photochemistry of the troposphere. Vertical profiles of tropospheric species were compared with the Leighton approximation, radiative transfer, matrix inversion model. The radiative transfer code includes the effects of multiple scattering due to molecules and aerosols, pure absorption, and surface albedo on the transfer of incoming solar radiation. It is indicated that significant differences exist for several key photolysis frequencies and species number density profiles between the Leighton approximation and the profiles generated with, radiative transfer, matrix inversion technique. Most species show enhanced vertical profiles when the more realistic treatment of the incoming solar radiation field is included

Augustsson, T. R.↗
NASA NTRS2008

Sparse Regression as a Sparse Eigenvalue Problem

We extend the l0-norm "subspectral" algorithms for sparse-LDA [5] and sparse-PCA [6] to general quadratic costs such as MSE in linear (kernel) regression. The resulting "Sparse Least Squares" (SLS) problem is also NP-hard, by way of its equivalence to a rank-1 sparse eigenvalue problem (e.g., binary sparse-LDA [7]). Specifically, for a general quadratic cost we use a highly-efficient technique for direct eigenvalue computation using partitioned matrix inverses which leads to dramatic x103 speed-ups over standard eigenvalue decomposition. This increased efficiency mitigates the O(n4) scaling behaviour that up to now has limited the previous algorithms' utility for high-dimensional learning problems. Moreover, the new computation prioritizes the role of the less-myopic backward elimination stage which becomes more efficient than forward selection. Similarly, branch-and-bound search for Exact Sparse Least Squares (ESLS) also benefits from partitioned matrix inverse techniques. Our Greedy Sparse Least Squares (GSLS) generalizes Natarajan's algorithm [9] also known as Order-Recursive Matching Pursuit (ORMP). Specifically, the forward half of GSLS is exactly equivalent to ORMP but more efficient. By including the backward pass, which only doubles the computation, we can achieve lower MSE than ORMP. Experimental comparisons to the state-of-the-art LARS algorithm [3] show forward-GSLS is faster, more accurate and more flexible in terms of choice of regularization

Exact Sparse Least Squares (ESLS)↗
NASA NTRS2007

Hybrid-dual-fourier tomographic algorithm for a fast three-dimensionial optical image reconstruction in turbid media

A reconstruction technique for reducing computation burden in the 3D image processes, wherein the reconstruction procedure comprises an inverse and a forward model. The inverse model uses a hybrid dual Fourier algorithm that combines a 2D Fourier inversion with a 1D matrix inversion to thereby provide high-speed inverse computations. The inverse algorithm uses a hybrid transfer to provide fast Fourier inversion for data of multiple sources and multiple detectors. The forward model is based on an analytical cumulant solution of a radiative transfer equation. The accurate analytical form of the solution to the radiative transfer equation provides an efficient formalism for fast computation of the forward model.

Alfano, Robert R.↗
NASA NTRS1971

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.↗
NASA NTRS1972

Statistical versus nonstatistical temperature inversion methods

Vertical temperature profiles are derived from radiation measurements by inverting the integral equation of radiative transfer. Because of the nonuniqueness of the solution, the particular temperature profile obtained depends on the numerical inversion technique used and the type of auxiliary information incorporated in the solution. The choice of an inversion algorithm depends on many factors; including the speed and size of computer, the availability of representative statistics, and the accuracy of initial data. Results are presented for a numerical study comparing two contrasting inversion methods: the statistical-matrix inversion method and the nonstatistical-iterative method. These were found to be the most applicable to the problem of determining atmospheric temperature profiles. Tradeoffs between the two methods are discussed.

Smith, W. L.↗