Review of Iterative Numerical Methods Preferred in Technical Application to Increase Efficiency

2020 ◽  
Author(s):  
Mustafa OZCAN ◽  
Fuad Aliew
Keyword(s):  
Numerical Methods ◽  
Technical Application ◽  
Iterative Numerical Methods ◽  
Increase Efficiency

scholarly journals Validation of Simulation Models without Knowledge of Parameters Using Differential Algebra

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Björn Haffke ◽  
Riccardo Möller ◽  
Tobias Melz ◽  
Jens Strackeljan
Keyword(s):  
System Identification ◽  
Numerical Methods ◽  
Nonlinear Systems ◽  
Differential Algebra ◽  
External Validation ◽  
Simulation Models ◽  
Input And Output ◽  
Iterative Numerical Methods

This study deals with the external validation of simulation models using methods from differential algebra. Without any system identification or iterative numerical methods, this approach provides evidence that the equations of a model can represent measured and simulated sets of data. This is very useful to check if a model is, in general, suitable. In addition, the application of this approach to verification of the similarity between the identifiable parameters of two models with different sets of input and output measurements is demonstrated. We present a discussion on how the method can be used to find parameter deviations between any two models. The advantage of this method is its applicability to nonlinear systems as well as its algorithmic nature, which makes it easy to automate.

scholarly journals On Some Iterative Numerical Methods for Mixed Volterra–Fredholm Integral Equations

Symmetry ◽  
2019 ◽  
Vol 11 (10) ◽  
pp. 1200
Author(s):  
Sanda Micula
Keyword(s):  
Numerical Methods ◽  
Integral Equations ◽  
Trapezoidal Rule ◽  
Picard Iteration ◽  
Fredholm Integral Equations ◽  
Convergence Conditions ◽  
One Dimensional ◽  
Cubature Formulas ◽  
Uniqueness Of The Solution ◽  
Iterative Numerical Methods

In this paper, we propose a class of simple numerical methods for approximating solutions of one-dimensional mixed Volterra–Fredholm integral equations of the second kind. These methods are based on fixed point results for the existence and uniqueness of the solution (results which also provide successive iterations of the solution) and suitable cubature formulas for the numerical approximations. We discuss in detail a method using Picard iteration and the two-dimensional composite trapezoidal rule, giving convergence conditions and error estimates. The paper concludes with numerical experiments and a discussion of the methods proposed.

scholarly journals Comparative Study of Various Iterative Numerical Methods for Computation of Approximate Root of the Polynomials

2021 ◽  
Vol 11 (2) ◽  
pp. 6-11
Author(s):  
Dr. Roopa K M ◽  
◽  
Venkatesha P ◽  
Keyword(s):  
Numerical Methods ◽  
Comparative Study ◽  
Iterative Methods ◽  
Numerical Comparison ◽  
Polynomial Equations ◽  
Chebyshev Method ◽  
Newton Raphson ◽  
Raphson Method ◽  
Iterative Numerical Methods

The aim of this article is to present a brief review and a numerical comparison of iterative methods applied to solve the polynomial equations with real coefficients. In this paper, four numerical methods are compared, namely: Horner’s method, Synthetic division with Chebyshev method (Proposed Method), Synthetic division with Modified Newton Raphson method and Birge-Vieta method which will helpful to the readers to understand the importance and usefulness of these methods.

scholarly journals Inverse Multiscale Discrete Radon Transform by Filtered Backprojection

2020 ◽  
Vol 11 (1) ◽  
pp. 22
Author(s):  
José G. Marichal-Hernández ◽  
Ricardo Oliva-García ◽  
Óscar Gómez-Cárdenes ◽  
Iván Rodríguez-Méndez ◽  
José M. Rodríguez-Ramos
Keyword(s):  
Numerical Methods ◽  
Inverse Problems ◽  
Iterative Methods ◽  
Radon Transform ◽  
Discrete Version ◽  
Filtered Backprojection ◽  
Discrete Radon Transform ◽  
First Time ◽  
The Sacrifice ◽  
Iterative Numerical Methods

The Radon transform is a valuable tool in inverse problems such as the ones present in electromagnetic imaging. Up to now the inversion of the multiscale discrete Radon transform has been only possible by iterative numerical methods while the continuous Radon transform is usually tackled with the filtered backprojection approach. In this study, we will show, for the first time, that the multiscale discrete version of Radon transform can as well be inverted with filtered backprojection, and by doing so, we will achieve the fastest implementation until now of bidimensional discrete Radon inversion. Moreover, the proposed method allows the sacrifice of accuracy for further acceleration. It is a well-conditioned inversion that exhibits a resistance against noise similar to that of iterative methods.

Sign in / Sign up

Export Citation Format

Share Document