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Results for “Iterative algorithms”

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 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

Distributed Minimal Residual (DMR) method for acceleration of iterative algorithms

A new method for enhancing the convergence rate of iterative algorithms for the numerical integration of systems of partial differential equations was developed. It is termed the Distributed Minimal Residual (DMR) method and it is based on general Krylov subspace methods. The DMR method differs from the Krylov subspace methods by the fact that the iterative acceleration factors are different from equation to equation in the system. At the same time, the DMR method can be viewed as an incomplete Newton iteration method. The DMR method was applied to Euler equations of gas dynamics and incompressible Navier-Stokes equations. All numerical test cases were obtained using either explicit four stage Runge-Kutta or Euler implicit time integration. The formulation for the DMR method is general in nature and can be applied to explicit and implicit iterative algorithms for arbitrary systems of partial differential equations.

Lee, Seungsoo↗
NASA NTRS1985

Performance of direct and iterative algorithms on an optical systolic processor

The frequency-multiplexed optical linear algebra processor (OLAP) is treated in detail with attention to its performance in the solution of systems of linear algebraic equations (LAEs). General guidelines suitable for most OLAPs, including digital-optical processors, are advanced concerning system and component error source models, guidelines for appropriate use of direct and iterative algorithms, the dominant error sources, and the effect of multiple simultaneous error sources. Specific results are advanced on the quantitative performance of both direct and iterative algorithms in the solution of systems of LAEs and in the solution of nonlinear matrix equations. Acoustic attenuation is found to dominate iterative algorithms and detector noise to dominate direct algorithms. The effect of multiple spatial errors is found to be additive. A theoretical expression for the amount of acoustic attenuation allowed is advanced and verified. Simulations and experimental data are included.

Ghosh, A. K.↗
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

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 NTRS1982

Iterative algorithms for large sparse linear systems on parallel computers

Algorithms for assembling in parallel the sparse system of linear equations that result from finite difference or finite element discretizations of elliptic partial differential equations, such as those that arise in structural engineering are developed. Parallel linear stationary iterative algorithms and parallel preconditioned conjugate gradient algorithms are developed for solving these systems. In addition, a model for comparing parallel algorithms on array architectures is developed and results of this model for the algorithms are given.

Adams, L. M.↗
DOE OSTI2023

Retrieval of temperature and humidity profiles from ground-based high-resolution infrared observations using an adaptive fast iterative algorithm

Various retrieval algorithms have been developed for retrieving temperature and water vapor profiles from Atmospheric Emitted Radiance Interferometer (AERI) observations. The physical retrieval algorithm, named AERI Optimal Estimation (AERIoe), outperforms other retrieval algorithms in many aspects except the retrieval time, which is significantly increased due to the complex radiative transfer process. The calculation of the Jacobian matrix is the most computationally intensive step of the physical retrieval algorithm. Interestingly, an analysis of the change in AERI observations' information content with respect to Jacobians revealed that the AERIoe algorithm's performance presents negligible dependence on these metrics. Thus, the Jacobian matrix could remain unchanged when the variation in the atmospheric state is small in the retrieval process to reduce the most time-consuming computation. On the basis of the above findings, a fast physical–iterative retrieval algorithm was proposed by adaptively recalculating Jacobians in keeping with the changes in the atmospheric state. Experiments with synthetic observations demonstrate that the proposed method experiences an average reduction in retrieval time by an impressive 59 % compared to the original AERIoe algorithm while achieving maximum root-mean-square errors of less than 0.95 K and 0.22 log(ppmv) for heights below 3 km for the temperature and water vapor profile, respectively. Further analyses revealed that the fast-retrieval algorithm reached an acceptable convergence rate of 98.7 %, marginally lower than AERIoe's 99.9 % convergence rate for the 826 cases used in this study.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1986

Simultaneous iterations algorithm for general eigenvalue problems on parallel processors

The method of simultaneous iteration with shift is extended to extraction of m-eigenpairs of a general eigenvalue problem of large order n in a parallel processing environment. The algorithm combines the power method and the Jacobi technique, and reduces to performing four basic operations. Parallel implementation of the algorithm is discussed in detail. The analysis accounts for computation and communication costs, and utilizes a parallel processing architecture of the ensemble type. Expressions for the computational efficiency and speedup are defined as a function of the problem and hardware parameters. Selected representative problems exhibit efficiencies ranging from 60 to 98 percent.

Utku, S.↗
NASA NTRS1984

Adapting iterative algorithms for solving large sparse linear systems for efficient use on the CDC CYBER 205

Adapting and designing mathematical software to achieve optimum performance on the CYBER 205 is discussed. Comments and observations are made in light of recent work done on modifying the ITPACK software package and on writing new software for vector supercomputers. The goal was to develop very efficient vector algorithms and software for solving large sparse linear systems using iterative methods.

Kincaid, D. R.↗
NASA NTRS1978

An iterative algorithm for decoding block codes transmitted over a memoryless channel

An algorithm was developed which optimally decodes a block code for minimum probability of symbol error in an iterative manner. The initial estimate is made by looking at each bit independently and is improved by considering bits related to it through the parity check equations. The dependent bits are considered in order of interesting probability of error. Since the computation proceeds in a systematic way with the bits having the greatest effect being used first, the algorithm approaches the optimum estimate after only a fraction of the parity check equations were used.

Greenberger, H. J.↗
NASA NTRS1984

A model of asynchronous iterative algorithms for solving large, sparse, linear systems

Solving large, sparse, linear systems of equations is one of the fundamental problems in large scale scientific and engineering computation. A model of a general class of asynchronous, iterative solution methods for linear systems is developed. In the model, the system is solved by creating several cooperating tasks that each compute a portion of the solution vector. This model is then analyzed to determine the expected intertask data transfer and task computational complexity as functions of the number of tasks. Based on the analysis, recommendations for task partitioning are made. These recommendations are a function of the sparseness of the linear system, its structure (i.e., randomly sparse or banded), and dimension.

Reed, D. A.↗
NASA NTRS1976

An iterative algorithm for objective wind field analysis

Three different algorithms for objective wind field analysis were tested on the same set of initial conditions: Dickerson-Sasaki's 'strong constraint' algorithm, a fixed-vorticity algorithm, and a newly proposed fixed-station-velocity algorithm. The three methods are compared with respect to the degree of minimization of wind divergence and the accuracy of wind data at a measured station. The first two techniques, though they reduce wind divergence, produce wind vectors substantially different from the observed values. The proposed iterative scheme is similar to Endlich's (1967) procedure for treating a macroscale wind field, and minimizes divergence while retaining the observed wind vectors.

Liu, C. Y.↗
NASA NTRS1990

An iterative algorithm combining model reduction and control design

A design strategy which integrates model reduction by modal cost analysis and a multiobjective controller design is proposed. The necessary modeling and control algorithms are easily programmed in Matlab standard software. Hence, this method is very practical for controller design for large space structures. The design algorithm also solves the very important problem of tuning multiple loop controllers (multi-input, multi-output, or MIMO). Instead of the single gain change that is used in standard root locus and gain and phase margin theories, this method tunes multiple loop controllers from low to high gain in a systematic way in the design procedure. This design strategy is applied to NASA's Mini-Mast system.

Hsieh, C.↗
NASA NTRS1998

Trellises and Trellis-Based Decoding Algorithms for Linear Block Codes: An Iterative Decoding Algorithm for Linear Block Codes Based on a Low-Weight Trellis Search - Part 3

For long linear block codes, maximum likelihood decoding based on full code trellises would be very hard to implement if not impossible. In this case, we may wish to trade error performance for the reduction in decoding complexity. Sub-optimum soft-decision decoding of a linear block code based on a low-weight sub-trellis can be devised to provide an effective trade-off between error performance and decoding complexity. This chapter presents such a suboptimal decoding algorithm for linear block codes. This decoding algorithm is iterative in nature and based on an optimality test. It has the following important features: (1) a simple method to generate a sequence of candidate code-words, one at a time, for test; (2) a sufficient condition for testing a candidate code-word for optimality; and (3) a low-weight sub-trellis search for finding the most likely (ML) code-word.

Lin, Shu↗
NASA NTRS1991

Phase retrieval for the Hubble Space Telescope using iterative propagation algorithms

Phase retrieval algorithms, including the iterative transform algorithm and gradient search algorithms, were generalized to include the effects of propagation through a complicated optical system and to discount the effects of bad CCD pixels. For the gradient search algorithms, analytic gradients were derived that greatly speed up the computation over finite difference methods. For the Hubble Space Telescope (HST), the aperture function was reconstructed and the phase errors were retrieved. This information is useful to design correction optics for the telescope and for the deconvolution of blurred images from the HST.

Fienup, J. R.↗
DOE OSTI2021

GPU-accelerated multitiered iterative phasing algorithm for fluctuation X-ray scattering

The multitiered iterative phasing (MTIP) algorithm is used to determine the biological structures of macromolecules from fluctuation scattering data. It is an iterative algorithm that reconstructs the electron density of the sample by matching the computed fluctuation X-ray scattering data to the external observations, and by simultaneously enforcing constraints in real and Fourier space. This paper presents the first ever MTIP algorithm acceleration efforts on contemporary graphics processing units (GPUs). The Compute Unified Device Architecture (CUDA) programming model is used to accelerate the MTIP algorithm on NVIDIA GPUs. The computational performance of the CUDA-based MTIP algorithm implementation outperforms the CPU-based version by an order of magnitude. Furthermore, the Heterogeneous-Compute Interface for Portability (HIP) runtime APIs are used to demonstrate portability by accelerating the MTIP algorithm across NVIDIA and AMD GPUs.

97 MATHEMATICS AND COMPUTING↗