Absolute x-ray energy calibration over a wide energy range using a diffraction-based iterative method
Abstract not provided
Hong, Xinguo↗
SEARCH · Engineering Papers
Results for “Iterative methods”
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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Comparative Analysis of Soft-Error Detection Strategies: A Case Study with Iterative Methods
Undetected soft errors caused by transient bit flips can lead to silent data corruption (SDC), an undesirable outcome where invalid results pass for valid ones. This has motivated the design of soft error detectors to minimize SDCs. However, the detectors have been studied under different contexts, making comparative evaluation difficult. In this paper, we present the first comprehensive evaluation of four online soft error detection techniques in detecting the adverse impact of soft errors on iterative methods. We observe that, across five iterative methods, the detectors studied achieve high but not perfect detection rates. To understand the potential for improved detection, we evaluate a machine-learning based detector that takes as features that are the runtime features observed by the individual detectors to arrive at their conclusions. Our evaluation demonstrates improved but still far from perfect detection accuracy for the machine learning based detectors. This extensive evaluation demonstrates the need for designing error detectors to handle the evolutionary behavior exhibited by iterative solvers.
Silent data corruption, Soft error detection, Iter↗
Analysis of Monte Carlo accelerated iterative methods for sparse linear systems: Analysis of Monte Carlo accelerated iterative methods for sparse linear systems
Here, we consider hybrid deterministic-stochastic iterative algorithms for the solution of large, sparse linear systems. Starting from a convergent splitting of the coefficient matrix, we analyze various types of Monte Carlo acceleration schemes applied to the original preconditioned Richardson (stationary) iteration. We expect that these methods will have considerable potential for resiliency to faults when implemented on massively parallel machines. We also establish sufficient conditions for the convergence of the hybrid schemes, and we investigate different types of preconditioners including sparse approximate inverses. Numerical experiments on linear systems arising from the discretization of partial differential equations are presented.
97 MATHEMATICS AND COMPUTING↗
Annual Copper Mountain Conferences on Multigrid and Iterative Methods, Copper Mountain, Colorado
This project supported the Copper Mountain Conference on Multigrid and Iterative Methods, held from 2007 to 2015, at Copper Mountain, Colorado. The subject of the Copper Mountain Conference Series alternated between Multigrid Methods in odd-numbered years and Iterative Methods in even-numbered years. Begun in 1983, the Series represents an important forum for the exchange of ideas in these two closely related fields. This report describes the Copper Mountain Conference on Multigrid and Iterative Methods, 2007-2015. Information on the conference series is available at http://grandmaster.colorado.edu/~copper/.
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
On semi-convergence and inexact iteration of the GSS iteration method for nonsymmetric singular saddle point problems
In this paper, the generalized shift-splitting (GSS) iteration method is used to solve nonsymmetric singular saddle point systems with the positive real (1, 1)-block sub-matrix. By a careful analysis of the spectral properties of the corresponding iteration matrix, we investigate the semi-convergence property of the GSS iteration method, give the sharper bounds of the eigenvalues for the GSS iteration method and propose the inexact GSS iteration method, also. Numerical experiments are given to show the correctness of the theoretical analysis and the feasibility of the GSS preconditioner with appropriate parameters.
97 MATHEMATICS AND COMPUTING↗
Nonlocal transport in bounded two-dimensional systems: An iterative method
Here, the concept of transport mediated through the dynamics of 'jumping' particles is used to develop an iterative method for obtaining steady-state solutions to the nonlocal transport equation in two dimensions (2D). The technique is self-adjoint and capable of correctly treating spatially non-uniform, asymmetric systems. An appropriate reduced version of the iteration method is used to compare with results obtained with a self-adjoint 1D transport matrix approach. The transport 'jump' probability distribution functions (pdfs) are based on Lévy α-stable distributions. The technique can handle the entire Lévy α-parameter range from one (Lorentz distributions) to two (Gaussian distributions). Cases with α = 2 (standard diffusion) are used to establish the validity of the iterative method. The capabilities of the iterative method are demonstrated by presenting examples from systems with various source configurations, boundary shapes, boundary conditions and spatial variations in parameters.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Factorizations of hyperpower family of iterative methods via least squares approach
A new method for finding proper factorizations of the hyperpower family of iterative methods for computing generalized inverses is proposed. The method is based on numerical optimization of an appropriate least squares problem. An iterative method in a non-normalized form for finding the generalized outer inverses with prescribed range and null space of any given complex matrix is proposed and considered. Computational complexity and convergence of the method are studied. Several numerical experiments are also presented.
97 MATHEMATICS AND COMPUTING↗
Ground-Truth Prediction to Accelerate Soft-Error Impact Analysis for Iterative Methods
Understanding the impact of soft errors on applications can be expensive. Often, it requires an extensive error injection campaign involving numerous runs of the full application in the presence of errors. In this paper, we present a novel approach to arriving at the ground truth--the true impact of an error on the final output--for iterative methods by observing a small number of iterations to learn deviations between normal and error-impacted execution. We develop a machine learning based predictor for three iterative methods to generate ground-truth results without running them to completion for every error injected. We demonstrate that this approach achieves greater accuracy than alternative prediction strategies, including three existing soft error detection strategies. We demonstrate the effectiveness of the ground truth prediction model in evaluating vulnerability and the effectiveness of soft error detection strategies in the context of iterative methods.
iterative methods, failure prediction, Soft error ↗
An iterative method for computing a symplectic SVD-like decomposition
In this paper, we present an effective iterative method for computing symplectic SVD-like decomposition for a 2n-by-m rectangular real matrix A. The main purpose here is a block-power iterative method with the ortho-symplectic SR decomposition in the normalization step. We compute an k-block symplectic SVD-like decomposition, namely A{sub k}=S{sub k}Σ{sub k}V{sub k}{sup T} where S{sub k}∈ℝ{sup 2n×2k} is symplectic and V{sub k}∈ℝ{sup m×2k} is orthogonal. For large matrices, we usually have to compute only part of eigenvalues. The main interest of the proposed method is to efficiently compute the desired number of ordered in magnitude eigenvalues of structured matrices.
97 MATHEMATICS AND COMPUTING↗
Stability Analysis of Inline ZFP Compression for Floating-Point Data in Iterative Methods
Currently, the dominating constraint in many high performance computing applications is data capacity and bandwidth, in both internode communications and even moreso in intranode data motion. A new approach to address this limitation is to make use of data compression in the form of a compressed data array. Storing data in a compressed data array and converting to standard IEEE-754 types as needed during a computation can reduce the pressure on bandwidth and storage. However, repeated conversions (lossy compression and decompression) introduce additional approximation errors, which need to be shown to not significantly affect the simulation results. Here, we extend recent work that analyzed the error of a single use of compression and decompression of the ZFP compressed data array representation to the case of time-stepping and iterative schemes, where an advancement operator is repeatedly applied in addition to the conversions. We show that the accumulated error for iterative methods involving fixed-point and time evolving iterations is bounded under standard constraints. An upper bound is established on the number of additional iterations required for the convergence of stationary fixed-point iterations. An additional analysis of traditional forward and backward error of stationary iterative methods using ZFP compressed arrays is also presented. The results of several 1D, 2D, and 3D test problems are provided to demonstrate the correctness of the theoretical bounds.
97 MATHEMATICS AND COMPUTING↗
Iterative methods for solving nonlinear problems of nuclear reactor criticality
The paper presents iterative methods for calculating the neutron flux distribution in nonlinear problems of nuclear reactor criticality. Algorithms for solving equations for variations in the neutron flux are considered. Convergence of the iterative processes is studied for two nonlinear problems in which macroscopic interaction cross sections are functionals of the spatial neutron distribution. In the first problem, the neutron flux distribution depends on the water coolant density, and in the second one, it depends on the fuel temperature. Simple relationships connecting the vapor content and the temperature with the neutron flux are used.
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
Characterization of the Impact of Soft Errors on Iterative Methods
Soft errors caused by transient bit flips have the potential to significantly impact an application’s behavior. This has motivated the design of an array of techniques to detect, isolate, and correct soft errors using microarchitectural, architectural, compilation-based, or application-level techniques to minimize their impact on the executing application. The first step towards the design of good error detection/correction techniques involves an understanding of an application’s vulnerability to soft errors. In this paper, we present the first comprehensive characterization of the impact of soft errors on the convergence characteristics of six iterative methods using application-level fault injection. In particular, we consider the use of iterative methods to incrementally solve a linear systems of equations, which constitutes the core kernel in many scientific applications. We analyze the impact of soft errors in terms of the type of error (single- vs multi-bit), the distribution and location of bits affected, the data structure and the statement impacted, and variation with time. In addition to understanding the vulnerability of iterative solvers to soft errors, this characterization can aid the design of fault injection campaigns that ensure systematic coverage.
fault injection, iterative methods, Silent data co↗
Refinement of overlapping local/global iteration method based on Monte Carlo/p-CMFD calculations
In this paper, the overlapping local/global (OLG) iteration method based on Monte Carlo/p-CMFD calculations is refined in two aspects. One is the consistent use of estimators to generate homogenized scattering cross sections. Another is that the incident or exiting angular interval is divided into multi-angular bins to modulate albedo boundary conditions for local problems. Numerical tests show that, compared to the one angle bin case in a previous study, the four angle bin case shows significantly improved results. (authors)
97 MATHEMATICS AND COMPUTING↗
Block-Iterative Methods for 3D Constant-Coefficient Stencils on GPUs and Multicore CPUs
Block iterative methods are extremely important as smoothers for multigrid methods, as preconditioners for Krylov methods, and as solvers for diagonally dominant linear systems. Developing robust and efficient smoother algorithms suitable for current and evolving GPU and multicore CPU systems is a significant challenge. We address this issue in the case of constant-coefficient stencils arising in the solution of elliptic partial differential equations on structured 3D uniform and adaptively refined block structured grids. Robust, highly parallel implementations of block Jacobi and chaotic block Gauss-Seidel algorithms with exact inversion of the blocks are developed using different parallelization techniques. Experimental results for NVIDIA Fermi/Kepler GPUs and AMD multicore systems are presented.
97 MATHEMATICS AND COMPUTING↗
Accelerated modulus-based matrix splitting iteration method for a class of nonlinear complementarity problems
In this paper, we reformulate a class of nonlinear complementarity problems as the implicit fixed-point equations. We demonstrate accelerated modulus-based matrix splitting iteration method. We show their convergence by assuming that the system matrix is positive definite or the splitting of the system matrix are H{sub +}-compatible splitting and discuss the choice of the optimal parameter. Furthermore, we give two-step accelerated modulus-based matrix splitting iteration method, which may achieve higher computing efficiency. Numerical experiments are presented to show the effectiveness of the method.
97 MATHEMATICS AND COMPUTING↗
Stellar surface as low-rank modification in iterative methods for binary neutron stars
We present a new multidomain spectral method for the treatment of non-spherical stellar surfaces in iterative methods for binary neutron stars. A stellar surface changes throughout the course of an iterative solution, potentially stalling the convergence. Our method affords low-complexity updates of the relevant subdomain preconditioners, thereby avoiding such stalling. Unlike current collocation (or nodal) approaches for treating surfaces (which rely on coordinate transformations to ensure that stellar surfaces arise at subdomain boundaries), our approach requires no regridding or nontrivial Jacobians. For polytropes with an equation of state specified by an integer polytropic index, our method delivers exponential accuracy with increased truncation, although for “stiff” equations of state (e.g. fractional) it suffers from the same accuracy loss as current methods. We have presented an outline of our approach before, but here present details with numerical tests.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
On LPMHSS-based iteration methods for a class of weakly nonlinear systems
In this paper, for a class of the large sparse system of weakly nonlinear equations, combining separable property of the linear and nonlinear terms with the lopsided Hermitian and skew-Hermitian splitting (LHSS) of the coefficient matrix, the Picard-LPMHSS and nonlinear LPMHSS-like iteration methods are presented. Theoretical analysis shows that these methods are locally convergent under suitable conditions. Numerical results show that both Picard-LPMHSS and nonlinear LPMHSS-like iteration methods are feasible and effective for the large-scale system of weakly nonlinear equations.
97 MATHEMATICS AND COMPUTING↗