Search NASA⌕ Search

SEARCH · Search NASA

Results for “Matrix 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 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1977

Comparison of linear inversion methods by examination of the duality between iterative and inverse matrix methods

Linear numerical inversion methods applied to atmospheric remote sounding generally can be categorized in two ways: (1) iterative, and (2) inverse matrix methods. However, these two categories are not unrelated; a duality exists between them. In other words, given an iterative scheme, a corresponding inverse matrix method exists, and conversely. This duality concept is developed for the more familiar linear methods. The iterative duals are compared with the classical linear iterative approaches and their differences analyzed. The importance of the initial profile in all methods is stressed. Calculations using simulated data are made to compare accuracies and to examine the dependence of the solution on the initial profile.

Fleming, H. E.↗
NASA NTRS1977

Inverse solution of the pseudoscalar transfer equation through nonlinear matrix inversion

Nonlinear matrix inversion operators have been developed which, applied to observed radiances, infer maximal information regarding atmospheric scattering parameters and vertical distribution of radiant sources and sinks. The algorithm has the attractive feature of noise discrimination, attributing instrumental errors to extra-atmospheric sources.

King, J. I. F.↗
NASA NTRS1975

On the convergence of certain finite-difference schemes by an inverse-matrix method

The inverse-matrix method of analyzing the convergence of the solution of a given system of finite-difference equations to the solution of the corresponding system of partial-differential equations is discussed and generalized. The convergence properties of a time- and space-centered differencing of the diffusion equation are analyzed as well as a staggered grid differencing of the Cauchy-Riemann equations. These two schemes are significant since they serve as simplified model algorithms for two recently developed methods used to calculate nonlinear aerodynamic flows.

Steger, J. L.↗
NASA NTRS1988

A Strassen-Newton algorithm for high-speed parallelizable matrix inversion

Techniques are described for computing matrix inverses by algorithms that are highly suited to massively parallel computation. The techniques are based on an algorithm suggested by Strassen (1969). Variations of this scheme use matrix Newton iterations and other methods to improve the numerical stability while at the same time preserving a very high level of parallelism. One-processor Cray-2 implementations of these schemes range from one that is up to 55 percent faster than a conventional library routine to one that is slower than a library routine but achieves excellent numerical stability. The problem of computing the solution to a single set of linear equations is discussed, and it is shown that this problem can also be solved efficiently using these techniques.

Bailey, David H.↗
NASA NTRS1987

Optical implementation of an iterative algorithm for matrix inversion

The incorporation of a photorefractive gain element into a confocal Fabry-Perot processor, with a photorefractive BaTiO3 crystal in the feedback path providing the coherent image amplification, is discussed. The implementation of an iterative algorithm for matrix inversion is described, and its experimental implementation is demonstrated. It is shown that the BaTiO3 amplifier provides loss compensation and coherence restoration of the feedback signal, thereby increasing the effective number of iterations in the algorithm. Thus, the technique makes it possible to implement slowly converging (as well as rapidly converging) algorithms.

Rajbenbach, Henri↗
NASA NTRS1986

Performance comparisons on spatial lattice algorithm and direct matrix inverse method with application to adaptive arrays processing

Lattice algorithm has been employed in numerous adaptive filtering applications such as speech analysis/synthesis, noise canceling, spectral analysis, and channel equalization. In this paper the application to adaptive-array processing is discussed. The advantages are fast convergence rate as well as computational accuracy independent of the noise and interference conditions. The results produced by this technique are compared to those obtained by the direct matrix inverse method.

An, S. H.↗
NASA NTRS2007

General Matrix Inversion Technique for the Calibration of Electric Field Sensor Arrays on Aircraft Platforms

A matrix calibration procedure has been developed that uniquely relates the electric fields measured at the aircraft with the external vector electric field and net aircraft charge. The calibration method can be generalized to any reasonable combination of electric field measurements and aircraft. A calibration matrix is determined for each aircraft that represents the individual instrument responses to the external electric field. The aircraft geometry and configuration of field mills (FMs) uniquely define the matrix. The matrix can then be inverted to determine the external electric field and net aircraft charge from the FM outputs. A distinct advantage of the method is that if one or more FMs need to be eliminated or deemphasized [e.g., due to a malfunction), it is a simple matter to reinvert the matrix without the malfunctioning FMs. To demonstrate the calibration technique, data are presented from several aircraft programs (ER-2, DC-8, Altus, and Citation).

Mach, D. M.↗
NASA NTRS2006

General Matrix Inversion for the Calibration of Electric Field Sensor Arrays on Aircraft Platforms

We have developed a matrix calibration procedure that uniquely relates the electric fields measured at the aircraft with the external vector electric field and net aircraft charge. Our calibration method is being used with all of our aircraft/electric field sensing combinations and can be generalized to any reasonable combination of electric field measurements and aircraft. We determine a calibration matrix that represents the individual instrument responses to the external electric field. The aircraft geometry and configuration of field mills (FMs) uniquely define the matrix. The matrix can then be inverted to determine the external electric field and net aircraft charge from the FM outputs. A distinct advantage of the method is that if one or more FMs need to be eliminated or de-emphasized (for example, due to a malfunction), it is a simple matter to reinvert the matrix without the malfunctioning FMs. To demonstrate our calibration technique, we present data from several of our aircraft programs (ER-2, DC-8, Altus, Citation).

Mach, D. M.↗
NASA NTRS1984

On reduced matrix inversion for operator splitting methods

The element-splitting heat-conduction algorithm of Hughes et al. (1983) is modified using the dual-basis approach of Flanagan and Belytschko (1981). The size of the system to be solved is reduced, and the formulation of a stiffness matrix is avoided. The 2D application is demonstrated, and the feasibility of a 3D implementation is indicated.

Belytschko, T.↗
NASA NTRS1987

Optimal control of large space structures via generalized inverse matrix

Independent Modal Space Control (IMSC) is a control scheme that decouples the space structure into n independent second-order subsystems according to n controlled modes and controls each mode independently. It is well-known that the IMSC eliminates control and observation spillover caused when the conventional coupled modal control scheme is employed. The independent control of each mode requires that the number of actuators be equal to the number of modelled modes, which is very high for a faithful modeling of large space structures. A control scheme is proposed that allows one to use a reduced number of actuators to control all modeled modes suboptimally. In particular, the method of generalized inverse matrices is employed to implement the actuators such that the eigenvalues of the closed-loop system are as closed as possible to those specified by the optimal IMSC. Computer simulation of the proposed control scheme on a simply supported beam is given.

Nguyen, Charles C.↗