Search results for "Gradient method"
showing 10 items of 38 documents
IBSIMU: a three-dimensional simulation software for charged particle optics.
2010
A general-purpose three-dimensional (3D) simulation code IBSIMU for charged particle optics with space charge is under development at JYFL. The code was originally developed for designing a slit-beam plasma extraction and nanosecond scale chopping for pulsed neutron generator, but has been developed further and has been used for many applications. The code features a nonlinear FDM Poisson's equation solver based on fast stabilized biconjugate gradient method with ILU0 preconditioner for solving electrostatic fields. A generally accepted nonlinear plasma model is used for plasma extraction. Magnetic fields can be imported to the simulations from other programs. The particle trajectories are …
Covariant approximation averaging
2015
We present a new class of statistical error reduction techniques for Monte-Carlo simulations. Using covariant symmetries, we show that correlation functions can be constructed from inexpensive approximations without introducing any systematic bias in the final result. We introduce a new class of covariant approximation averaging techniques, known as all-mode averaging (AMA), in which the approximation takes account of contributions of all eigenmodes through the inverse of the Dirac operator computed from the conjugate gradient method with a relaxed stopping condition. In this paper we compare the performance and computational cost of our new method with traditional methods using correlation…
A Lagrange Multiplier Based Domain Decomposition Method for the Solution of a Wave Problem with Discontinuous Coefficients
2008
In this paper we consider the numerical solution of a linear wave equation with discontinuous coefficients. We divide the computational domain into two subdomains and use explicit time difference scheme along with piecewise linear finite element approximations on semimatching grids. We apply boundary supported Lagrange multiplier method to match the solution on the interface between subdomains. The resulting system of linear equations of the “saddle-point” type is solved efficiently by a conjugate gradient method.
Iterative Regularization Techniques in Image Reconstruction
2000
In this survey we review recent developments concerning the efficient iterative regularization of image reconstruction problems in atmospheric imaging. We present a number of preconditioners for the minimization of the corresponding Tikhonov functional, and discuss the alternative of terminating the iteration early, rather than adding a stabilizing term in the Tikhonov functional. The methods are examplified for a (synthetic) model problem.
Tridiagonal preconditioning for Poisson-like difference equations with flat grids: Application to incompressible atmospheric flow
2011
AbstractThe convergence of many iterative procedures, in particular that of the conjugate gradient method, strongly depends on the condition number of the linear system to be solved. In cases with a large condition number, therefore, preconditioning is often used to transform the system into an equivalent one, with a smaller condition number and therefore faster convergence. For Poisson-like difference equations with flat grids, the vertical part of the difference operator is dominant and tridiagonal and can be used for preconditioning. Such a procedure has been applied to incompressible atmospheric flows to preserve incompressibility, where a system of Poisson-like difference equations is …
About the finite convergence of the proximal point algorithm
1988
We study the finite convergence property of the proximal point algorithm applied to the partial inverse, with respect to a subspace, of the subdifferential of a polyhedral convex function. Using examples we show how sufficient conditions providing the finite convergence can be realized and we give a case with non finite termination.
QR-Factorization Algorithm for Computed Tomography (CT): Comparison With FDK and Conjugate Gradient (CG) Algorithms
2018
[EN] Even though QR-factorization of the system matrix for tomographic devices has been already used for medical imaging, to date, no satisfactory solution has been found for solving large linear systems, such as those used in computed tomography (CT) (in the order of 106 equations). In CT, the Feldkamp, Davis, and Kress back projection algorithm (FDK) and iterative methods like conjugate gradient (CG) are the standard methods used for image reconstruction. As the image reconstruction problem can be modeled by a large linear system of equations, QR-factorization of the system matrix could be used to solve this system. Current advances in computer science enable the use of direct methods for…
Optimizing auditory images and distance metrics for self‐organizing timbre maps*
1996
Abstract The effect of using different auditory images and distance metrics on the final configuration of a self‐organized timbre map is examined by comparing distance matrices, obtained from simulations, with a similarity rating matrix, obtained using the same set of stimuli as in the simulations. Gradient images, which are intended to represent idealizations of physiological gradient maps in the auditory pathway, are constructed. The optimal auditory image and distance metric, with respect to the similarity rating data, are searched using the gradient method.
A Mlp-Based Digit And Uppercase Characters Recognition System
1997
A simple software solution for digit and uppercase handwritten characters recognition is presented. The proposed solution is based on a two-layer Multi Layer Perceptron (MLP) trained by a conjugate gradient descent (CGD) optimization algorithm. This neural network is embedded in a software tool for automatic processing of forms achieved using a scanner. The chosen solutions allow us to obtain good results both in terms of recognition rate and speed. In the paper are fully described design details and experimental results.
Iterative moment method for electromagnetic transients in grounding systems on CRAY T3D
1996
In this paper the parallel aspects of an electromagnetic model for transients in grounding systems based on an iterative scheme are investigated in a multiprocessor environment. A coarse and fine grain parallel solutions have been developed on the CRAY T3D, housed at CINECA, equipped with 64 processors working in space sharing modality. The performances of the two parallel approaches implemented according to the work sharing parallel paradigm have been evaluated for different problem sizes employing variable number of processors.