An inverse-free Newton-Jarratt-type iterative method for solving equations under the gamma condition

2008 ◽  
Vol 28 (1-2) ◽  
pp. 15-28 ◽  
Author(s):  
Ioannis K. Argyros
Keyword(s):  
Iterative Method ◽  
Solving Equations

A fifth-order iterative method for solving equations

1987 ◽  
Vol 49 (1-2) ◽  
pp. 129-137 ◽  
Author(s):  
Duong Thuy Vy
Keyword(s):  
Iterative Method ◽  
Solving Equations ◽  
Fifth Order

A combined reordering procedure for preconditioned GMRES applied to solving equations using Lagrange multiplier method

2014 ◽  
Vol 31 (7) ◽  
pp. 1283-1304
Author(s):  
Zixiang Hu ◽  
Zhenmin Wang ◽  
Shi Zhang ◽  
Yun Zhang ◽  
Huamin Zhou
Keyword(s):  
Iterative Method ◽  
Lagrange Multiplier ◽  
Large Scale ◽  
Minimum Degree ◽  
Coefficient Matrix ◽  
Lagrange Multiplier Method ◽  
Multiplier Method ◽  
Content Type ◽  
Wide Range ◽  
Solving Equations

Purpose – The purpose of this paper is to propose a combined reordering scheme with a wide range of application, called Reversed Cuthill-McKee-approximate minimum degree (RCM-AMD), to improve a preconditioned general minimal residual method for solving equations using Lagrange multiplier method, and facilitates the choice of the reordering for the iterative method. Design/methodology/approach – To reordering the coefficient matrix before a preconditioned iterative method will greatly impact its convergence behavior, but the effect is very problem-dependent, even performs very differently when different preconditionings applied for an identical problem or the scale of the problem varies. The proposed reordering scheme is designed based on the features of two popular ordering schemes, RCM and AMD, and benefits from each of them. Findings – Via numerical experiments for the cases of various scales and difficulties, the effects of RCM-AMD on the preconditioner and the convergence are investigated and the comparisons of RCM, AMD and RCM-AMD are presented. The results show that the proposed reordering scheme RCM-AMD is appropriate for large-scale and difficult problems and can be used more generally and conveniently. The reason of the reordering effects is further analyzed as well. Originality/value – The proposed RCM-AMD reordering scheme preferable for solving equations using Lagrange multiplier method, especially considering that the large-scale and difficult problems are very common in practical application. This combined reordering scheme is more wide-ranging and facilitates the choice of the reordering for the iterative method, and the proposed iterative method has good performance for practical cases in in-house and commercial codes on PC.

scholarly journals On some iterative methods with frozen derivatives for solving equations

2021 ◽  
Vol 5 (1) ◽  
pp. 209-217
Author(s):  
Samundra Regmi ◽  
◽  
Christopher Argyros ◽  
Ioannis K. Argyros ◽  
Santhosh George ◽  
...  
Keyword(s):  
Banach Space ◽  
Iterative Method ◽  
Convergence Analysis ◽  
Iterative Methods ◽  
Radius Of Convergence ◽  
Numerical Examples ◽  
First Derivative ◽  
Solving Equations

We determine a radius of convergence for an efficient iterative method with frozen derivatives to solve Banach space defined equations. Our convergence analysis use \(\omega-\) continuity conditions only on the first derivative. Earlier studies have used hypotheses up to the seventh derivative, limiting the applicability of the method. Numerical examples complete the article.

Quality Improvement of X-ray CT Images by Estimation of the Mechanical Misalignment in a Projection Image Using an Iterative Method

2017 ◽  
Vol 137 (3) ◽  
pp. 213-219
Author(s):  
Kenji Noguchi ◽  
Satoshi Takahashi ◽  
Daisuke Suzuki ◽  
Atsushi Teramoto
Keyword(s):  
Quality Improvement ◽  
Iterative Method ◽  
Ct Images ◽  
X Ray ◽  
Projection Image

THE REALIZATION OF THE ITERATIVE METHOD OF THE LEAST SQUARES FOR THE ESTIMATION OF STATIC OBJECT PARAMETERS IN MATLAB ENVIRONMENT

2017 ◽  
pp. 28-36
Author(s):  
Galina Vasil’evna Troshina ◽  
Alexander Aleksandrovich Voevoda
Keyword(s):  
Parameter Estimation ◽  
Iterative Method ◽  
Least Squares ◽  
Input Signal ◽  
Layer Structure ◽  
Estimation Procedure ◽  
Parameter Estimation Procedure ◽  
Noise Simulation ◽  
Static Object ◽  
Object Parameters

It was suggested to use the system model working in real time for an iterative method of the parameter estimation. It gives the chance to select a suitable input signal, and also to carry out the setup of the object parameters. The object modeling for a case when the system isn't affected by the measurement noises, and also for a case when an object is under the gaussian noise was executed in the MatLab environment. The superposition of two meanders with different periods and single amplitude is used as an input signal. The model represents the three-layer structure in the MatLab environment. On the most upper layer there are units corresponding to the simulation of an input signal, directly the object, the unit of the noise simulation and the unit for the parameter estimation. The second and the third layers correspond to the simulation of the iterative method of the least squares. The diagrams of the input and the output signals in the absence of noise and in the presence of noise are shown. The results of parameter estimation of a static object are given. According to the results of modeling, the algorithm works well even in the presence of significant measurement noise. To verify the correctness of the work of an algorithm the auxiliary computations have been performed and the diagrams of the gain behavior amount which is used in the parameter estimation procedure have been constructed. The entry conditions which are necessary for the work of an iterative method of the least squares are specified. The understanding of this algorithm functioning principles is a basis for its subsequent use for the parameter estimation of the multi-channel dynamic objects.

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