scholarly journals The Convergence of a Class of Parallel Newton-Type Iterative Methods

2017 ◽  
Vol 2017 ◽  
pp. 1-7
Author(s):  
Qinglong Huang
Keyword(s):  
Iterative Methods ◽  
Convergence Theorem ◽  
Iterative Process ◽  
Numerical Example

A general iterative process is proposed, from which a class of parallel Newton-type iterative methods can be derived. A unified convergence theorem for the general iterative process is established. The convergence of these Newton-type iterative methods is obtained from the unified convergence theorem. The results of efficiency analyses and numerical example are satisfactory.

scholarly journals The alternate direction iterative methods for generalized saddle point systems

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Shuanghua Luo ◽  
Angang Cui ◽  
Cheng-yi Zhang
Keyword(s):  
Saddle Point ◽  
Iterative Methods ◽  
Iterative Schemes ◽  
Numerical Example ◽  
Convergence Results ◽  
Alternate Direction ◽  
Saddle Point Matrix

Abstract The paper studies two splitting forms of generalized saddle point matrix to derive two alternate direction iterative schemes for generalized saddle point systems. Some convergence results are established for these two alternate direction iterative methods. Meanwhile, a numerical example is given to show that the proposed alternate direction iterative methods are much more effective and efficient than the existing one.

scholarly journals A strong convergence theorem for a zero of the sum of a finite family of maximally monotone mappings

2020 ◽  
Vol 53 (1) ◽  
pp. 152-166 ◽  
Author(s):  
Getahun B. Wega ◽  
Habtu Zegeye ◽  
Oganeditse A. Boikanyo
Keyword(s):  
Strong Convergence ◽  
Approximation Method ◽  
Convergence Theorem ◽  
Finite Family ◽  
Strong Convergence Theorem ◽  
Monotone Mappings ◽  
Important Class ◽  
Numerical Example ◽  
Minimization Problems ◽  
Nonlinear Mappings

AbstractThe purpose of this article is to study the method of approximation for zeros of the sum of a finite family of maximally monotone mappings and prove strong convergence of the proposed approximation method under suitable conditions. The method of proof is of independent interest. In addition, we give some applications to the minimization problems and provide a numerical example which supports our main result. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear mappings.

SIMPLE YET EFFICIENT ALGORITHM FOR SOLVING NONLINEAR EQUATIONS

2010 ◽  
Vol 01 (04) ◽  
pp. 509-522
Author(s):  
SANJAY KUMAR KHATTRI ◽  
MUHAMMAD ASLAM NOOR
Keyword(s):  
Convergence Analysis ◽  
Iterative Methods ◽  
Newton Method ◽  
Efficient Algorithm ◽  
Iterative Process ◽  
Computational Results ◽  
Numerical Work ◽  
Software Packages ◽  
Practical Algorithm ◽  
Convergence Orders

In this work, we develop a simple yet robust and highly practical algorithm for constructing iterative methods of higher convergence orders. The algorithm can be easily implemented in software packages for achieving desired convergence orders. Convergence analysis shows that the algorithm can develop methods of various convergence orders which is also supported through the numerical work. The algorithm is shown to converge even if the derivative of the function vanishes during the iterative process. Computational results ascertain that the developed algorithm is efficient and demonstrate equal or better performance as compared with other well known methods and the classical Newton method.

A New Testability Optimization Allocation Approach

2013 ◽  
Vol 328 ◽  
pp. 444-449 ◽  
Author(s):  
Gang Liu ◽  
Fang Li
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Iterative Process ◽  
Resource Constraints ◽  
Optimal Solution ◽  
Improved Genetic Algorithm ◽  
Numerical Example ◽  
Set Up ◽  
Optimization Allocation ◽  
Allocation Approach

This paper describes a methodology based on improved genetic algorithms (GA) and experiments plan to optimize the testability allocation. Test resources were reasonably configured for testability optimization allocation, in order to meet the testability allocation requirements and resource constraints. The optimal solution was not easy to solve of general genetic algorithm, and the initial parameter value was not easy to set up and other defects. So in order to more efficiently test and optimize the allocation, migration technology was introduced in the traditional genetic algorithm to optimize the iterative process, and initial parameters of algorithm could be adjusted by using AHP approach, consequently testability optimization allocation approach based on improved genetic algorithm was proposed. A numerical example is used to assess the method. and the examples show that this approach can quickly and efficiently to seek the optimal solution of testability optimization allocation problem.

scholarly journals Convergence analysis for combination of equilibrium problems and k-nonspreading multi-valued mappings

2021 ◽  
Author(s):  
Suhel Ahmad Khan ◽  
Kaleem Raza Kazmi ◽  
Watcharaporn Cholamjiak ◽  
Hemen Dutta
Keyword(s):  
Strong Convergence ◽  
Fixed Points ◽  
Convergence Analysis ◽  
Hybrid Method ◽  
Convergence Theorem ◽  
Equilibrium Problems ◽  
Solution Set ◽  
Strong Convergence Theorem ◽  
Numerical Example ◽  
Common Solution

We prove a strong convergence theorem for finding a common solution of a combination of equilibrium problems and the set of fixed points of a k-nonspreading multi-valued mapping by using shrinking projection hybrid method. Further, we give a numerical example to justify our main result and compare the shrinking areas of solution set after randomization.

scholarly journals Dynamics of Host-Parasite Models with Harvesting of Parasites and Partial Cover for Host

2020 ◽  
Vol 9 (3) ◽  
pp. 1436-1440
Keyword(s):  
Experimental Investigation ◽  
Theoretical Model ◽  
Mathematical Models ◽  
Iterative Methods ◽  
Host Species ◽  
Iterative Process ◽  
Crucial Element ◽  
Partial Cover ◽  
And Mathematics ◽  
Host Parasite

Modeling might be viewed like a knowledge concerning with the communication among other topics and mathematics, theoretical discipline on a number of elements of the daily world. Mathematical models take to be crucial resources in iterative methods and biological investigations of info collection. Mathematical models take to be crucial resources in bioticsurveys with an iterative process of info collection. The experimental investigation as well as the theoretical model is usually a crucial element in developing tests and in the interpretation of information. Parasites are actually the organisms which feed on their hosts or host immediately upon it, at some point resulting in the death of host species.

scholarly journals Deferred correction for the integral equation eigenvalue problem

1981 ◽  
Vol 22 (4) ◽  
pp. 474-487 ◽  
Author(s):  
K. W. Chu ◽  
A. Spence
Keyword(s):  
Integral Equation ◽  
Eigenvalue Problem ◽  
Integral Equations ◽  
Convergence Theorem ◽  
Eigenvalues And Eigenfunctions ◽  
Deferred Correction ◽  
Numerical Example

AbstractThis paper considers the improvement of approximate eigenvalues and eigenfunctions of integral equations using the method of deferred correction. A convergence theorem is proved and a numerical example illustrating the theory is given.

scholarly journals A path convergence theorem and construction of fixed points for nonexpansive mappings in certain Banach spaces

2016 ◽  
Vol 32 (2) ◽  
pp. 241-250
Author(s):  
T. M. M. SOW ◽  
◽  
N. DJITTE ◽  
C.E. CHIDUME ◽  
◽  
...  
Keyword(s):  
Strong Convergence ◽  
Fixed Points ◽  
Banach Spaces ◽  
Convergence Theorem ◽  
Iterative Process ◽  
Nonexpansive Mappings ◽  
Convergence Theorems ◽  
Nonexpansive Maps ◽  
Weakly Continuous ◽  
Duality Map

In this paper, we introduce a new iterative process to approximate fixed points of nonexpansive maps in real Banach spaces having weakly continuous duality map and establish strong convergence theorems for the proposed iterative process. There is no compactness assumption on K or on T. Our results improve important recent results.

scholarly journals DETERMINATION OF GEODESIC LATITUDE BY SPATIAL RIGHT-MUGAL COORDINATES BY USING A DIFFERENTIAL AMENDMENT

2019 ◽  
Vol 1 (2) ◽  
pp. 3-8
Author(s):  
Konstantin Afonin ◽  
Yulia Trifonova
Keyword(s):  
Iterative Methods ◽  
Practical Application ◽  
Third Way ◽  
Differential Correction ◽  
Numerical Example ◽  
The Third ◽  
Rectangular Coordinates

GNSS technologies are currently essential for coordinate support of territories. However, theymakeit possible to obtain spatial rectangular coordinates of the points being determined. While most users need the flat rectangular coordinates of Gauss – Kruger. And these coordinates can be calculated only by geodetic latitudes and longitudes. The special literature describes more than a dozen methods for calculating the geodetic latitude in spatial rectangular coordinates. To solve this problem, usually use any iterative or non-iterative methods. Both those and others have their ad-vantages and disadvantages. In the work applied the third way to solve the problem. It is proposed to calculate and use the differential correction to the initial (approximate) value of the geodesic lati-tude. Received working formulas that implement this idea. A numerical example is given showing the possibility of practical application oftheproposedmethod.

Comparison Results between Jacobi and USSOR Iterative Methods

2014 ◽  
Vol 989-994 ◽  
pp. 1790-1793
Author(s):  
Ting Zhou ◽  
Shi Guang Zhang
Keyword(s):  
Linear Systems ◽  
Iterative Methods ◽  
Spectral Radius ◽  
Numerical Example ◽  
Iteration Matrix ◽  
Comparison Results ◽  
Jacobi Iteration

In this paper, some comparison results between Jacobi and USSOR iteration for solving nonsingular linear systems are presented. It is showed that spectral radius of Jacobi iteration matrix B is less than that of USSOR iterative matrix under some conditions. A numerical example is also given to illustrate our results.

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