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Results for “Inverse Multiplication”

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 NTRS1979

Inverse multiple scattering problems. III - Inadequacy of certain limb darkening and phase curves for retrieving atmospheric information and limitations of approximate scattering models

The paper considers three complementary inverse multiple scattering problems relating to a uniquely defined atmospheric scattering model. Consideration is given to the appropriateness, for data inversion purposes, of intensities observed in diffuse reflection under a variety of experimental conditions; the uniqueness of the inverse solution is investigated. It is found that light curves representing monotonic variations, such as limb darkening curves and phase curves for a planetary (e.g., Venus) disk center are unsuitable for inferring atmospheric and scattering parameters.

Fymat, A. L.↗
NASA NTRS1985

VLSI architectures for computing multiplications and inverses in GF(2m)

Finite field arithmetic logic is central in the implementation of Reed-Solomon coders and in some cryptographic algorithms. There is a need for good multiplication and inversion algorithms that are easily realized on VLSI chips. Massey and Omura recently developed a new multiplication algorithm for Galois fields based on a normal basis representation. A pipeline structure is developed to realize the Massey-Omura multiplier in the finite field GF(2m). With the simple squaring property of the normal-basis representation used together with this multiplier, a pipeline architecture is also developed for computing inverse elements in GF(2m). The designs developed for the Massey-Omura multiplier and the computation of inverse elements are regular, simple, expandable and, therefore, naturally suitable for VLSI implementation.

Wang, C. C.↗
NASA NTRS1983

VLSI architectures for computing multiplications and inverses in GF(2-m)

Finite field arithmetic logic is central in the implementation of Reed-Solomon coders and in some cryptographic algorithms. There is a need for good multiplication and inversion algorithms that are easily realized on VLSI chips. Massey and Omura recently developed a new multiplication algorithm for Galois fields based on a normal basis representation. A pipeline structure is developed to realize the Massey-Omura multiplier in the finite field GF(2m). With the simple squaring property of the normal-basis representation used together with this multiplier, a pipeline architecture is also developed for computing inverse elements in GF(2m). The designs developed for the Massey-Omura multiplier and the computation of inverse elements are regular, simple, expandable and, therefore, naturally suitable for VLSI implementation.

Wang, C. C.↗
NASA NTRS1991

On designing for quality

The problem of ensuring the required quality of products and/or technological processes often becomes more difficult due to the fact that there is not general theory of determining the optimal sets of value of the primary factors, i.e., of the output parameters of the parts and units comprising an object and ensuring the correspondence of the object's parameters to the quality requirements. This is the main reason for the amount of time taken to finish complex vital article. To create this theory, one has to overcome a number of difficulties and to solve the following tasks: the creation of reliable and stable mathematical models showing the influence of the primary factors on the output parameters; finding a new technique of assigning tolerances for primary factors with regard to economical, technological, and other criteria, the technique being based on the solution of the main problem; well reasoned assignment of nominal values for primary factors which serve as the basis for creating tolerances. Each of the above listed tasks is of independent importance. An attempt is made to give solutions for this problem. The above problem dealing with quality ensuring an mathematically formalized aspect is called the multiple inverse problem.

Vajingortin, L. D.↗
NASA NTRS1981

Remote sensing of temperature profiles in vegetation canopies using multiple view angles and inversion techniques

A mathematical method is presented which allows the determination of vertical temperature profiles of vegetation canopies from multiple sensor view angles and some knowledge of the vegetation geometric structure. The technique was evaluated with data from several wheat canopies at different stages of development, and shown to be most useful in the separation of vegetation and substrate temperatures with greater accuracy in the case of intermediate and dense vegetation canopies than in sparse ones. The converse is true for substrate temperatures. Root-mean-square prediction accuracies of temperatures for intermediate-density wheat canopies were 1.8 C and 1.4 C for an exact and an overdeterminate system, respectively. The findings have implication for remote sensing research in agriculture, geology or other earth resources disciplines.

Kimes, D. S.↗
NASA NTRS1972

Application of stepwise multiple regression techniques to inversion of Nimbus 'IRIS' observations.

Exploratory studies with Nimbus-3 infrared interferometer-spectrometer (IRIS) data indicate that, in addition to temperature, such meteorological parameters as geopotential heights of pressure surfaces, tropopause pressure, and tropopause temperature can be inferred from the observed spectra with the use of simple regression equations. The technique of screening the IRIS spectral data by means of stepwise regression to obtain the best radiation predictors of meteorological parameters is validated. The simplicity of application of the technique and the simplicity of the derived linear regression equations - which contain only a few terms - suggest usefulness for this approach. Based upon the results obtained, suggestions are made for further development and exploitation of the stepwise regression analysis technique.

Ohring, G.↗
NASA NTRS1979

On the multiplicity of solutions of the inverse problem for a vibrating beam

The paper considers a specific inverse problem for a vibrating beam with three nonsympathetic spectra. More specifically, the spectral data consist of the natural frequencies of vibration of the beam in the following three configurations: (1) clamped-clamped, (2) clamped-supported, and (3) clamped-free. The basic equations for an inhomogeneous discrete beam are derived, where this simple mechanical system provides valuable insight into the inverse problem. All the necessary ingredients for a consideration of the inverse problem are given. Attention is given to an analysis of the particular inverse problem for which the spectral data are associated with the natural frequencies of vibrations in the above configurations. It is shown that with such data, the inverse problem has a 2exp(N-1)-fold multiplicity of solutions.

Barcilon, V.↗
NASA NTRS1992

LAI inversion from optical reflectance using a neural network trained with a multiple scattering model

The inversion of the leaf area index (LAI) canopy parameter from optical spectral reflectance measurements is obtained using a backpropagation artificial neural network trained using input-output pairs generated by a multiple scattering reflectance model. The problem of LAI estimation over sparse canopies (LAI < 1.0) with varying soil reflectance backgrounds is particularly difficult. Standard multiple regression methods applied to canopies within a single homogeneous soil type yield good results but perform unacceptably when applied across soil boundaries, resulting in absolute percentage errors of >1000 percent for low LAI. Minimization methods applied to merit functions constructed from differences between measured reflectances and predicted reflectances using multiple-scattering models are unacceptably sensitive to a good initial guess for the desired parameter. In contrast, the neural network reported generally yields absolute percentage errors of <30 percent when weighting coefficients trained on one soil type were applied to predicted canopy reflectance at a different soil background.

Smith, James A.↗
NASA NTRS1992

Inversion of snow parameters from passive microwave remote sensing measurements by a neural network trained with a multiple scattering model

Simultaneous inversion of the three parameters was performed which included mean-grain size of ice particles in snow, snow density, and snow temperatures from five brightness temperatures. Good results for the inversion of parameters were obtained using the neural network based on the simulated data computed from the dense media radiative transfer equation that takes into account the effects of multiple scattering.

Tsang, Leung↗
NASA NTRS1983

Matrix differentiation formulas

A compact differentiation technique (without using indexes) is developed for scalar functions that depend on complex matrix arguments which are combined by operations of complex conjugation, transposition, addition, multiplication, matrix inversion and taking the direct product. The differentiation apparatus is developed in order to simplify the solution of extremum problems of scalar functions of matrix arguments.

Usikov, D. A.↗
NASA NTRS1986

Multiplier Architecture for Coding Circuits

Multipliers based on new algorithm for Galois-field (GF) arithmetic regular and expandable. Pipeline structures used for computing both multiplications and inverses. Designs suitable for implementation in very-large-scale integrated (VLSI) circuits. This general type of inverter and multiplier architecture especially useful in performing finite-field arithmetic of Reed-Solomon error-correcting codes and of some cryptographic algorithms.

Wang, C. C.↗
NASA NTRS1988

Control strategies

Techniques for improving the performance of robotic-manipulator path-control systems comprising independent SISO feedback controllers for each joint are discussed and illustrated with block diagrams, reviewing the results of recent analytical investigations. Topics examined include the servo design for a single link, the equations of motion for manipulators, SISO servo design for multiple links, inverse methods, pole placement with compensation of the gravity terms, linear state-feedback control based on the perturbation equations, and adaptive control methods. Consideration is given to variable-structure systems, suboptimal controllers, and the optimal-design-strategy approach.

Wang, J. C.↗
NASA NTRS2003

Meshless Local Petrov-Galerkin Euler-Bernoulli Beam Problems: A Radial Basis Function Approach

A radial basis function implementation of the meshless local Petrov-Galerkin (MLPG) method is presented to study Euler-Bernoulli beam problems. Radial basis functions, rather than generalized moving least squares (GMLS) interpolations, are used to develop the trial functions. This choice yields a computationally simpler method as fewer matrix inversions and multiplications are required than when GMLS interpolations are used. Test functions are chosen as simple weight functions as in the conventional MLPG method. Compactly and noncompactly supported radial basis functions are considered. The non-compactly supported cubic radial basis function is found to perform very well. Results obtained from the radial basis MLPG method are comparable to those obtained using the conventional MLPG method for mixed boundary value problems and problems with discontinuous loading conditions.

Raju, I. S.↗
NASA NTRS2004

A Meshless Method Using Radial Basis Functions for Beam Bending Problems

A meshless local Petrov-Galerkin (MLPG) method that uses radial basis functions (RBFs) as trial functions in the study of Euler-Bernoulli beam problems is presented. RBFs, rather than generalized moving least squares (GMLS) interpolations, are used to develop the trial functions. This choice yields a computationally simpler method as fewer matrix inversions and multiplications are required than when GMLS interpolations are used. Test functions are chosen as simple weight functions as they are in the conventional MLPG method. Compactly and noncompactly supported RBFs are considered. Noncompactly supported cubic RBFs are found to be preferable. Patch tests, mixed boundary value problems, and problems with complex loading conditions are considered. Results obtained from the radial basis MLPG method are either of comparable or better accuracy than those obtained when using the conventional MLPG method.

Raju, I. S.↗
NASA NTRS1997

Interpretation of Trace Gas Data Using Inverse Methods and Global Chemical Transport Models

This is a theoretical research project aimed at: (1) development, testing, and refining of inverse methods for determining regional and global transient source and sink strengths for long lived gases important in ozone depletion and climate forcing, (2) utilization of inverse methods to determine these source/sink strengths which use the NCAR/Boulder CCM2-T42 3-D model and a global 3-D Model for Atmospheric Transport and Chemistry (MATCH) which is based on analyzed observed wind fields (developed in collaboration by MIT and NCAR/Boulder), (3) determination of global (and perhaps regional) average hydroxyl radical concentrations using inverse methods with multiple titrating gases, and, (4) computation of the lifetimes and spatially resolved destruction rates of trace gases using 3-D models. Important goals include determination of regional source strengths of methane, nitrous oxide, and other climatically and chemically important biogenic trace gases and also of halocarbons restricted by the Montreal Protocol and its follow-on agreements and hydrohalocarbons used as alternatives to the restricted halocarbons.

Prinn, Ronald G.↗
NASA NTRS1999

[Global Atmospheric Chemistry/Transport Modeling and Data-Analysis]

This grant supported a global atmospheric chemistry/transport modeling and data- analysis project devoted to: (a) development, testing, and refining of inverse methods for determining regional and global transient source and sink strengths for trace gases; (b) utilization of these inverse methods which use either the Model for Atmospheric Chemistry and Transport (MATCH) which is based on analyzed observed winds or back- trajectories calculated from these same winds for determining regional and global source and sink strengths for long-lived trace gases important in ozone depletion and the greenhouse effect; (c) determination of global (and perhaps regional) average hydroxyl radical concentrations using inverse methods with multiple "titrating" gases; and (d) computation of the lifetimes and spatially resolved destruction rates of trace gases using 3D models. Important ultimate goals included determination of regional source strengths of important biogenic/anthropogenic trace gases and also of halocarbons restricted by the Montreal Protocol and its follow-on agreements, and hydrohalocarbons now used as alternatives to the above restricted halocarbons.

Prinn, Ronald G.↗