The Iteration Function on NetPad

2019 ◽  
Author(s):  
Jie Wang ◽  
Yongsheng Rao ◽  
Ruxian Chen ◽  
Hao Guan ◽  
Ying Wang ◽  
...  
Keyword(s):  
Iteration Function

scholarly journals A New Family of High-Order Ehrlich-Type Iterative Methods

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1855 ◽  
Author(s):  
Petko D. Proinov ◽  
Maria T. Vasileva
Keyword(s):  
Iterative Methods ◽  
Local Convergence ◽  
Semilocal Convergence ◽  
High Order ◽  
Convergence Theorems ◽  
New Family ◽  
Special Cases ◽  
Iteration Functions ◽  
Iteration Function ◽  
Local Convergence Analysis

One of the famous third-order iterative methods for finding simultaneously all the zeros of a polynomial was introduced by Ehrlich in 1967. In this paper, we construct a new family of high-order iterative methods as a combination of Ehrlich’s iteration function and an arbitrary iteration function. We call these methods Ehrlich’s methods with correction. The paper provides a detailed local convergence analysis of presented iterative methods for a large class of iteration functions. As a consequence, we obtain two types of local convergence theorems as well as semilocal convergence theorems (with computer verifiable initial condition). As special cases of the main results, we study the convergence of several particular iterative methods. The paper ends with some experiments that show the applicability of our semilocal convergence theorems.

scholarly journals Convergence Ball and Complex Geometry of an Iteration Function of Higher Order

Mathematics ◽  
2018 ◽  
Vol 7 (1) ◽  
pp. 28 ◽  
Author(s):  
Deepak Kumar ◽  
Ioannis Argyros ◽  
Janak Sharma
Keyword(s):  
Complex Geometry ◽  
Basins Of Attraction ◽  
Higher Order ◽  
Order Method ◽  
Eighth Order ◽  
Science And Engineering ◽  
Convergence Ball ◽  
Convergence Results ◽  
Iteration Function ◽  
Derivatives Of

Higher-order derivatives are used to determine the convergence order of iterative methods. However, such derivatives are not present in the formulas. Therefore, the assumptions on the higher-order derivatives of the function restrict the applicability of methods. Our convergence analysis of an eighth-order method uses only the derivative of order one. The convergence results so obtained are applied to some real problems, which arise in science and engineering. Finally, stability of the method is checked through complex geometry shown by drawing basins of attraction of the solutions.

An algorithm for the total, or partial, factorization of a polynomial

1977 ◽  
Vol 82 (3) ◽  
pp. 427-437 ◽  
Author(s):  
M. R. Farmer ◽  
G. Loizou
Keyword(s):  
Numerical Results ◽  
Search Procedure ◽  
Multiple Zeros ◽  
Globally Convergent ◽  
Simultaneous Iteration ◽  
Accelerate Convergence ◽  
Iteration Function ◽  
Convergent Algorithm

AbstractA globally convergent algorithm is presented for the total, or partial, factorization of a polynomial. Firstly, a circle is found containing all the zeros. Secondly, a search procedure locates smaller circles, each containing a zero, and the multiplicities are then calculated. Thirdly, a simultaneous Iteration Function is used to accelerate convergence. The Iteration Function is chosen from a class of such functions derived herein to deal with the general case of multiple zeros; various properties of these functions are also discussed. Finally, sample numerical results are given which demon-strate the effectiveness of the algorithm.

scholarly journals Regenerasi Fungsi x2-9x-99 Dalam Pembangkit Bilangan Acak Berbasis CSRPNG Chaos

AITI ◽  
2020 ◽  
Vol 16 (2) ◽  
pp. 125-134
Author(s):  
David Lihananto ◽  
Alz Danny Wowor
Keyword(s):  
Fixed Point ◽  
Iteration Method ◽  
Quadratic Function ◽  
Random Numbers ◽  
Fixed Point Iteration ◽  
Iteration Function ◽  
Run Test ◽  
Randomization Testing ◽  
Correlation Level

This study examines whether the function f(x)=x2-9x-99 can be used as a key generator in cryptography. The quadratic function is regenerated using the fixed point iteration method into an iteration function. The distribution of digits to the output of iterative function to generate a number of chaos. Randomization testing uses run test and monobit testing. Followed by cryptographic testing to get the correlation between ciphertext and key which will be used as a decision whether the resulting key is random or not. Based on research that has been done iteration function xi = (xi-12-9xi-1-99)/9 can generate CSRPNG Chaos random numbers with the correlation level closest to the value of 0.

scholarly journals Experiment Research on the Inverse Presumption Method to Evaluate Peak Temperature for Post-fire Spatial Structure

2017 ◽  
Vol 11 (1) ◽  
pp. 831-838
Author(s):  
Jing Cui ◽  
Lingfeng Yin ◽  
Xiaoming Guo ◽  
Gan Tang
Keyword(s):  
Temperature Field ◽  
Spatial Structure ◽  
Structural Damage ◽  
Inverse Method ◽  
Steel Structures ◽  
Peak Temperature ◽  
Residual Displacements ◽  
Iteration Function ◽  
The Difference ◽  
In Fire

Introduction: The peak temperature is one of the most important factors to evaluate the structural damage. Due to the reduction in the tensile strength of the steel, the structural stress is redistributed and the bearing capacity is decreased at the elevated temperature. Methods: This paper presents an inverse method to evaluate the peak temperature for the steel structures subjected to fire. An initial temperature field is assumed based on the post-fire structural residual displacement, and a temperature iteration function is developed to approach the peak temperature of the structure in fire by minimizing the difference between the measured and numerical results. An experimental study was conducted to investigate the structural behavior of a spatial structure subjected to fire. The temperature and displacement data were recorded. Result and Conclusion: Results show that the measured results have a good agreement with the predicted results, demonstrating that the proposed method in this paper is available for evaluate the peak temperature with a desirable accuracy. The inverse method of the temperature field can provide a theoretical basis for scientifically evaluating the residual displacements of the post-fire structure and formulating reliable repair and reinforcement schemes.

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