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At least 163 records · Page 9

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NASA NTRS1980

Incorporation of star measurements for the determination of orbit and attitude parameters of a geosynchronous satellite: An iterative application of linear regression

Currently on NOAA/NESS's VIRGS system at the World Weather Building star images are being ingested on a daily basis. The image coordinates of the star locations are measured and stored. Subsequently, the information is used to determine the attitude, the misalignment angles between the spin axis and the principal axis of the satellite, and the precession rate and direction. This is done for both the 'East' and 'West' operational geosynchronous satellites. This orientation information is then combined with image measurements of earth based landmarks to determine the orbit of each satellite. The method for determining the orbit is simple. For each landmark measurement one determines a nominal position vector for the satellite by extending a ray from the landmark's position towards the satellite and intersecting the ray with a sphere with center coinciding with the Earth's center and with radius equal to the nominal height for a geosynchronous satellite. The apparent motion of the satellite around the Earth's center is then approximated with a Keplerian model. In turn the variations of the satellite's height, as a function of time found by using this model, are used to redetermine the successive satellite positions by again using the Earth based landmark measurements and intersecting rays from these landmarks with the newly determined spheres. This process is performed iteratively until convergence is achieved. Only three iterations are required.

Phillips, D.↗

NASA NTRS1980

Iterative methods based upon residual averaging

Iterative methods for solving boundary value problems for systems of nonlinear partial differential equations are discussed. The methods involve subtracting an average of residuals from one approximation in order to arrive at a subsequent approximation. Two abstract methods in Hilbert space are given and application of these methods to quasilinear systems to give numerical schemes for such problems is demonstrated. Potential theoretic matters related to the iteration schemes are discussed.

Neuberger, J. W.↗

NASA NTRS1980

Iterative solutions for one-dimensional diffusion with time varying surface composition and composition-dependent diffusion coefficient

Solutions are given for one-dimensional diffusion problems with a time varying surface composition and also a composition dependent diffusion coefficient. The most general solution does not require special mathematical functions to fit the variation in surface composition or D(C). In another solution, a series expansion may be used to fit the time dependent surface concentration. These solutions make use of iterative calculations that converge rapidly and are highly stable. Computer times are much shorter than that required for finite difference calculations and can efficiently make use of interactive graphics terminals. Existing gas carburization data were used to provide an illustration of an iterative approach with a time varying carbon composition at the free surface.

Chow, M.↗

NASA NTRS1983

Minimizing inner product data dependencies in conjugate gradient iteration

The amount of concurrency available in conjugate gradient iteration is limited by the summations required in the inner product computations. The inner product of two vectors of length N requires time c log(N), if N or more processors are available. This paper describes an algebraic restructuring of the conjugate gradient algorithm which minimizes data dependencies due to inner product calculations. After an initial start up, the new algorithm can perform a conjugate gradient iteration in time c*log(log(N)).

Vanrosendale, J.↗

NASA NTRS1983

An iterative method for the Helmholtz equation

An iterative algorithm for the solution of the Helmholtz equation is developed. The algorithm is based on a preconditioned conjugate gradient iteration for the normal equations. The preconditioning is based on an SSOR sweep for the discrete Laplacian. Numerical results are presented for a wide variety of problems of physical interest and demonstrate the effectiveness of the algorithm.

Bayliss, A.↗

NASA NTRS1983

An iterative approach to region growing using associative memories

Region growing, often given as a classical example of the recursive control structures used in image processing which are often awkward to implement in hardware where the intent is the segmentation of an image at raster scan rates, is addressed in light of the postulate that any computation which can be performed recursively can be performed easily and efficiently by iteration coupled with association. Attention is given to an algorithm and hardware structure able to perform region labeling iteratively at scan rates. Every pixel is individually labeled with an identifier which signifies the region to which it belongs. Difficulties otherwise requiring recursion are handled by maintaining an equivalence table in hardware transparent to the computer, which reads the labeled pixels. A simulation of the associative memory has demonstrated its effectiveness.

Snyder, W. E.↗

NASA NTRS1985

Picard iterations of boundary-layer equations

A method of solving the boundary-layer equations that arise in singular-perturbation analysis of flightpath optimization problems is presented. The method is based on Picard iterations of the integrated form of the equations and does not require iteration to find unknown boundary conditions. As an example, the method is used to develop a solution algorithm for the zero-order boundary-layer equations of the aircraft minimum-time-to-climb problem.

Ardema, M. D.↗

NASA NTRS1985

Convergence acceleration of iterative solutions of Euler equations for transonic flow computations

In this paper, two acceleration techniques for Euler calculations are investigated. The first technique is an extrapolation procedure based on the Power Method; it is applicable when the iterative matrix has dominant eigenvalues. Both real and complex conjugate roots are allowed. The second technique is a generalization of the Minimal Residual Method, where the extrapolation step consists of a weighted combination of the corrections at different iteration levels and the weights are chosen to minimize the Lz norm of the residual. Numerical results, using Jameson's Runge-Kutta Multigrid Code, are presented. The extra computational work to apply either technique is negligible and the extra storage is not a problem on current supercomputers.

Hafez, M.↗

NASA NTRS1985

Sensitivity calculations for iteratively solved problems

The calculation of sensitivity derivatives of solutions of iteratively solved systems of algebraic equations is investigated. A modified finite difference procedure is presented which improves the accuracy of the calculated derivatives. The procedure is demonstrated for a simple algebraic example as well as an element-by-element preconditioned conjugate gradient iterative solution technique applied to truss examples.

Haftka, R. T.↗

NASA NTRS1985

A Study of Morrison's Iterative Noise Removal Method

Morrison's iterative noise removal method is studied by characterizing its effect upon systems of differing noise level and response function. The nature of data acquired from a linear shift invariant instrument is discussed so as to define the relationship between the input signal, the instrument response function, and the output signal. Fourier analysis is introduced, along with several pertinent theorems, as a tool to more thorough understanding of the nature of and difficulties with deconvolution. In relation to such difficulties the necessity of a noise removal process is discussed. Morrison's iterative noise removal method and the restrictions upon its application are developed. The nature of permissible response functions is discussed, as is the choice of the response functions used.

Ioup, G. E.↗

NASA NTRS1985

Iterative solution of large, sparse linear systems on a static data flow architecture - Performance studies

The applicability of static data flow architectures to the iterative solution of sparse linear systems of equations is investigated. An analytic performance model of a static data flow computation is developed. This model includes both spatial parallelism, concurrent execution in multiple PE's, and pipelining, the streaming of data from array memories through the PE's. The performance model is used to analyze a row partitioned iterative algorithm for solving sparse linear systems of algebraic equations. Based on this analysis, design parameters for the static data flow architecture as a function of matrix sparsity and dimension are proposed.

Reed, D. A.↗

NASA NTRS1985

Solution algorithms for nonlinear transient heat conduction analysis employing element-by-element iterative strategies

The particular problems investigated in the present study arise from nonlinear transient heat conduction. One of two types of nonlinearities considered is related to a material temperature dependence which is frequently needed to accurately model behavior over the range of temperature of engineering interest. The second nonlinearity is introduced by radiation boundary conditions. The finite element equations arising from the solution of nonlinear transient heat conduction problems are formulated. The finite element matrix equations are temporally discretized, and a nonlinear iterative solution algorithm is proposed. Algorithms for solving the linear problem are discussed, taking into account the form of the matrix equations, Gaussian elimination, cost, and iterative techniques. Attention is also given to approximate factorization, implementational aspects, and numerical results.

Winget, J. M.↗

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 NTRS1987

Optimal application of Morrison's iterative noise removal for deconvolution. Appendices

Morrison's iterative method of noise removal, or Morrison's smoothing, is applied in a simulation to noise-added data sets of various noise levels to determine its optimum use. Morrison's smoothing is applied for noise removal alone, and for noise removal prior to deconvolution. For the latter, an accurate method is analyzed to provide confidence in the optimization. The method consists of convolving the data with an inverse filter calculated by taking the inverse discrete Fourier transform of the reciprocal of the transform of the response of the system. Various length filters are calculated for the narrow and wide Gaussian response functions used. Deconvolution of non-noisy data is performed, and the error in each deconvolution calculated. Plots are produced of error versus filter length; and from these plots the most accurate length filters determined. The statistical methodologies employed in the optimizations of Morrison's method are similar. A typical peak-type input is selected and convolved with the two response functions to produce the data sets to be analyzed. Both constant and ordinate-dependent Gaussian distributed noise is added to the data, where the noise levels of the data are characterized by their signal-to-noise ratios. The error measures employed in the optimizations are the L1 and L2 norms. Results of the optimizations for both Gaussians, both noise types, and both norms include figures of optimum iteration number and error improvement versus signal-to-noise ratio, and tables of results. The statistical variation of all quantities considered is also given.

Ioup, George E.↗

NASA NTRS1987

Array architectures for iterative algorithms

Regular mesh-connected arrays are shown to be isomorphic to a class of so-called regular iterative algorithms. For a wide variety of problems it is shown how to obtain appropriate iterative algorithms and then how to translate these algorithms into arrays in a systematic fashion. Several 'systolic' arrays presented in the literature are shown to be specific cases of the variety of architectures that can be derived by the techniques presented here. These include arrays for Fourier Transform, Matrix Multiplication, and Sorting.

Jagadish, Hosagrahar V.↗

NASA NTRS1987

A hypermatrix formulation for subspace iteration

The computational efficiency of subspace iteration is addressed relative to the data structures adopted for the very large and generally sparse coefficient matrices. The frequent triangulations and matrix multiplications demand that access to the terms in the coefficient matrices be unbiased. Reliance on virtual memory (paging) operating systems with no special considerations for localized data access is not adequate. Specific data structures must be designed that accommodate the needs of the numerical algorithm yet eliminate unnecessary paging. An implementation of the subspace iteration method using hypermatrix data structures is presented. Use of hypermatrices is shown to provide unbiased and localized data access. The various modifications to the conventional formulation are described and an example problem illustrates the potential benefits of the hypermatrix formulation. Possibilities for adapting hypermatrix data structures to new supercomputer architectures are discussed.

Schmidt, Richard J.↗

NASA NTRS1989

Iterative methods for design sensitivity analysis

A numerical method is presented for design sensitivity analysis, using an iterative-method reanalysis of the structure generated by a small perturbation in the design variable; a forward-difference scheme is then employed to obtain the approximate sensitivity. Algorithms are developed for displacement and stress sensitivity, as well as for eignevalues and eigenvector sensitivity, and the iterative schemes are modified so that the coefficient matrices are constant and therefore decomposed only once.

Belegundu, A. D.↗

NASA NTRS1989

An iterative method for systems of nonlinear hyperbolic equations

An iterative algorithm for the efficient solution of systems of nonlinear hyperbolic equations is presented. Parallelism is evident at several levels. In the formation of the iteration, the equations are decoupled, thereby providing large grain parallelism. Parallelism may also be exploited within the solves for each equation. Convergence of the interation is established via a bounding function argument. Experimental results in two-dimensions are presented.

Scroggs, Jeffrey S.↗