Application Of Conjugate Gradient Method Research Articles

The Application of Conjugate Gradient Methods to Optimize 3D Printed Parameters

The Application of Conjugate Gradient Methods to Optimize 3D Printed Parameters

Signal recovery with convex constrained nonlinear monotone equations through conjugate gradient hybrid approach

In recent years there is a vast application of conjugate gradient methods to restore the disturbed signals in compressive sensing. This research aims at developing a scheme, which is more effective for restoring disturbed signals than the popular PCG method (Liu & Li, 2015). To realize the desired goal, a new conjugate gradient approach combined with the projection scheme of Solodov and Svaiter [Kluwer Academic Publishers, pp. 355-369(1998)] for solving monotone nonlinear equations with convex constraints is presented. The main idea employed in this algorithm is to approximate the Jacobian matrix via acceleration parameter in order to propose an effective conjugate gradient parameter. In addition, the step length is calculated using inexact line search technique. The proposed approach is proved to converge globally under some mild conditions . The numerical experiment, depicts the efficacy our method. Apart from generating search directions that are vital for global convergence, a significant contribution of the new method lies in its applications to solve the ℓ1-norm regularization problem in signal recovery. Experiments with the scheme and the effective PCG solver, existing in the previous literature, shows that the new method provides much better results.

An application of conjugate gradient method under strong Wolfe line search for solving unconstrained optimization

The conjugate gradient (CG) method is one of the most prominent methods for solving linear and nonlinear problems in optimization. In this paper, we propose a CG method with sufficient descent property under strong Wolfe line search. The proposed CG method is then applied to solve systems of linear equations. The numerical results obtained from the tests are evaluated based on number iteration and CPU time and then analyzed through performance profile. In order to examine its efficiency, the performance of our CG formula is compared to that of other CG methods. The results show that the proposed CG formula has better performance than the other tested CG methods.

A data processing method in the experiment of heat flux testing using inverse methods

The model of axisymmetric heat conduction with the application of Conjugate Gradient Method, Sequential Function Method is adopted to establish a robust, accurate and well-posed method of data processing fit for coaxial thermocouple measuring heat flux. Simulation and stability analysis are made in which four classic function forms of heat flux are estimated to illustrate accuracy, stability, as well as factors of influencing quality of these two parameter estimation methods. Subsequently, a bulb experiment for validation is made, with the analysis of error caused by installation of coaxial thermocouple sensor on experiment model through numerical calculation. All these demonstrate that this data processing method using inverse methods can improve the accuracy of testing very well.

Comparative application of CGM and Wiener filtering techniques for the estimation of heat flux distribution

The conjugate gradient method (CGM), formulated with the adjoint problem, is adopted in this study as the functional minimization tool for the solution of the 2-D steady-state linear inverse heat conduction problem with the aim of estimating the heat flux density distribution on a given surface using the temperature distribution as input data. The robustness of the solution strategy, based on an iterative regularization scheme, is compared with another consolidated estimation methodology adopted in the literature to handle the same problem: the Wiener filtering technique. The comparison is performed by adopting a noisy test signal aimed at simulating infrared temperature maps. Using a comparative approach, the problem's particular difficulties related to the high number of unknowns and to the deficiency of the estimation techniques at the domain's geometrical boundaries are discussed.

Application of conjugate gradient method for static problems involving conductors of arbitrary shape

In this paper, two implementations of the Conjugate Gradient Method (CGM) for the solution of problems in electrostatics involving conductors of arbitrary shapes have been discussed. The first method uses a least squares approximation for the computation of the pertinent integral operator and is referred to as LSD. A second implementation, referred to as Point Matching Discretisation (PMD) effects considerable saving in the computer time since it uses the midpoint rule for the integral arising in LSD. Both these techniques require O(N) storage, where N is the number of patches used to model the conductor. Further, a matrix interpretation of the present formulation has been derived. This has facilitated the comparison of the techniques described in this paper with the well known Method of Moments (MoM) formulation and has led to better understanding of the convergence of the results. Using illustrative examples of canonical (square and circular discs) and arbitrary shape (a pyramid mounted on a cube), the convergence of and the computer time for both the implementations have been investigated. It has been shown that both the techniques yielded monotonically convergent results for all the examples considered and that the LSD offers better estimate of the capacitance than PMD with lower number of patches. >

The application of conjugate gradient methods to NLTE rate matrix equations

This paper brings to attention recent developments in algorithms to efficiently solve linear systems resulting from the discretization of systems of population rate equations which arise in X-ray laser kinetics modeling. Specifically, we report the success of two variants of the preconditioned gradient method, namely the preconditioned conjugate gradient square (PCGS) algorithm and the method of generalized conjugate residuals (GCR) in solving non-LTE rate equations.