ESTIMATION OF NON-STATIONARY PARAMETERS OF NONLINEAR EQUATIONS UNDER UNCERTAINTY

2019 ◽  
Author(s):  
Oleksandr Nakonechnyi ◽  
Petro Zinko ◽  
Iulia Shevchuk
Keyword(s):  
Interpersonal Communication ◽  
Nonlinear Equations ◽  
Numerical Experiments ◽  
Linear Equations ◽  
Subject Area ◽  
System Of Nonlinear Equations ◽  
Social Community ◽  
Non Linear ◽  
Number Of Individuals ◽  
Communicative Space

This paper presents research of system of nonlinear equations. The algorithms of building a priory estimations, optimal functional estimations and guaranteed estimations of non-stationary parameters of differential equations are offered. These results are spread for discrete-time models. The algorithms of building optimal estimations and guaranteed estimations of non-stationary parameters of difference non-linear equations are offered. The approaches to construct optimal estimations based on Bellman functions and Kalman-Bussi filter. For each algorithms of building optimal functional estimations and guaranteed estimations the error of estimation are offered. We have presented as an example the results of numerical experiments to build guaranteed and optimal estimates for mathematical model of spreading one type of information with external influence. The number of information is taken as key parameter promoting accomplishment of aim. Information is spread in the community along internal (interpersonal communication of the members of social community) and external threads (mass media). Also for simplicity models with a constant number of individuals who are intentionally able to perceive and further spread an informational massage are explored. The model takes the form of non-linear ordinary differential equation with stationary parameters. The peculiarity of such models is that they allow a reasonable level of precision to model the subject area and obtain he results that can be uses in practice. The numerical experiments demonstrated the practical meaning of offered results. The offered approaches except theoretical interest has an important practical meaning. The results can be useful for algorithm development for estimation of dynamic of process in the information-communicative space.

Quantum Newton’s Method for Solving the System of Nonlinear Equations

SPIN ◽  
2021 ◽  
pp. 2140004
Author(s):  
Cheng Xue ◽  
Yuchun Wu ◽  
Guoping Guo
Keyword(s):  
Quantum Computing ◽  
Nonlinear Equations ◽  
Newton’S Method ◽  
Newton's Method ◽  
Linear Equations ◽  
Data Conversion ◽  
System Of Nonlinear Equations ◽  
Dimensional System ◽  
System Of Linear Equations ◽  
Whole Process

While quantum computing provides an exponential advantage in solving the system of linear equations, there is little work to solve the system of nonlinear equations with quantum computing. We propose quantum Newton’s method (QNM) for solving [Formula: see text]-dimensional system of nonlinear equations based on Newton’s method. In QNM, we solve the system of linear equations in each iteration of Newton’s method with quantum linear system solver. We use a specific quantum data structure and [Formula: see text] tomography with sample error [Formula: see text] to implement the classical-quantum data conversion process between the two iterations of QNM, thereby constructing the whole process of QNM. The complexity of QNM in each iteration is [Formula: see text]. Through numerical simulation, we find that when [Formula: see text], QNM is still effective, so the complexity of QNM is sublinear with [Formula: see text], which provides quantum advantage compared with the optimal classical algorithm.

scholarly journals A New Higher-Order Iterative Scheme for the Solutions of Nonlinear Systems

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 271 ◽  
Author(s):  
Ramandeep Behl ◽  
Ioannis K. Argyros
Keyword(s):  
Mathematical Modeling ◽  
Banach Space ◽  
Nonlinear Equations ◽  
Numerical Experiments ◽  
Iterative Scheme ◽  
Real Life ◽  
System Of Nonlinear Equations ◽  
Life Problems ◽  
Lipschitz Constants ◽  
Better Than

Many real-life problems can be reduced to scalar and vectorial nonlinear equations by using mathematical modeling. In this paper, we introduce a new iterative family of the sixth-order for a system of nonlinear equations. In addition, we present analyses of their convergences, as well as the computable radii for the guaranteed convergence of them for Banach space valued operators and error bounds based on the Lipschitz constants. Moreover, we show the applicability of them to some real-life problems, such as kinematic syntheses, Bratu’s, Fisher’s, boundary value, and Hammerstein integral problems. We finally wind up on the ground of achieved numerical experiments, where they perform better than other competing schemes.

Some the Application of the Taylor Series for the Analysis of Processes in Non-Linear Resistive Circuits

2014 ◽  
Vol 701-702 ◽  
pp. 1173-1176
Author(s):  
Vitaly Viktorovich Pivnev ◽  
Sergey Nikolaevich Basan
Keyword(s):  
Power Series ◽  
Nonlinear Equations ◽  
Taylor Series ◽  
System Of Nonlinear Equations ◽  
Algebraic Equations ◽  
Electrical Circuits ◽  
It Implementation ◽  
Linear Algebraic Equations ◽  
Non Linear ◽  
The Way

The way of calculating the currents and voltages in nonlinear resistive electrical circuits , based on the use of power series (Taylor, Maclaurin) is considered . The advantage of this method lies in the fact that while it implementation it is not necessary to a system of nonlinear equations. To determine the numerical values ​​of the coefficients of the power series corresponding system of linear algebraic equations are solved. Nonlinear operations are limited to the calculation of the numerical values ​​of currents, voltages and their derivatives with respect to the pole equations of nonlinear elements.

scholarly journals Finding the Roots of System of Nonlinear Equations by a Novel Filled Function Method

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
Wei-Xiang Wang ◽  
You-Lin Shang ◽  
Wei-Gang Sun ◽  
Ying Zhang
Keyword(s):  
Nonlinear Equations ◽  
Numerical Experiments ◽  
Function Method ◽  
Optimization Problem ◽  
Test Problems ◽  
System Of Nonlinear Equations ◽  
Global Optimization Problem ◽  
Filled Function ◽  
Filled Function Method ◽  
Constrained System

We present a novel filled function approach to solve box-constrained system of nonlinear equations. The system is first transformed into an equivalent nonsmooth global minimization problem, and then a new filled function method is proposed to solve this global optimization problem. Numerical experiments on several test problems are conducted and the computational results are also reported.

scholarly journals An Improved Line Search Filter Method for the System of Nonlinear Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Zhong Jin ◽  
Yuqing Wang
Keyword(s):  
Global Convergence ◽  
Objective Function ◽  
Nonlinear Equations ◽  
Numerical Experiments ◽  
Line Search ◽  
Equality Constraints ◽  
Filter Method ◽  
System Of Nonlinear Equations ◽  
Search Filter

An improved line search filter algorithm for the system of nonlinear equations is presented. We divide the equations into two groups, one contains the equations that are treated as equality constraints and the square of other equations is regarded as objective function. Two groups of equations are updated at every iteration in the works by Nie (2004, 2006, and 2006), by Nie et al. (2008), and by Gu (2011), while we just update them at the iterations when it is needed indeed. As a consequence, the scale of the calculation is decreased in a certain degree. Under some suitable conditions the global convergence can be induced. In the end, numerical experiments show that the method in this paper is effective.

scholarly journals A New High-Order and Efficient Family of Iterative Techniques for Nonlinear Models

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Ramandeep Behl ◽  
Eulalia Martínez
Keyword(s):  
Convergence Analysis ◽  
Nonlinear Equations ◽  
Numerical Experiments ◽  
Free Parameter ◽  
Nonlinear Models ◽  
High Order ◽  
System Of Nonlinear Equations ◽  
Iterative Technique ◽  
Order Convergence ◽  
Validity And Reliability

In this paper, we want to construct a new high-order and efficient iterative technique for solving a system of nonlinear equations. For this purpose, we extend the earlier scalar scheme [16] to a system of nonlinear equations preserving the same convergence order. Moreover, by adding one more additional step, we obtain minimum 5th-order convergence for every value of a free parameter, θ∈ℝ, and for θ=−1, the method reaches maximum 6-order convergence. We present an extensive convergence analysis of our scheme. The analytical discussion of the work is upheld by performing numerical experiments on some applied science problems and a large system of nonlinear equations. Furthermore, numerical results demonstrate the validity and reliability of the suggested methods.

EMAHAMAN METODE NUMERIK (STUDI KASUS METODE NEW-RHAPSON) MENGGUNAKAN PEMPROGRMAN MATLAB

2017 ◽  
Vol 1 (1) ◽  
pp. 95
Author(s):  
Siti Nurhabibah Hutagalung
Keyword(s):  
Numerical Methods ◽  
Theoretical Analysis ◽  
Nonlinear Equations ◽  
Linear Equations ◽  
Non Linear ◽  
Newton Raphson ◽  
Raphson Method ◽  
Non Linear Equations

Abstract - The study of the characteristics of non-liier functions can be carried out experimentally and theoretically. One part of theoretical analysis is computation. For computational purposes, numerical methods can be used to solve equations complicated, for example non-linear equations. There are a number of numerical methods that can be used to solve nonlinear equations, the Newton-Raphson method. Keywords - Numerical, Newton Raphson.

scholarly journals A Nonmonotone Line Search Filter Algorithm for the System of Nonlinear Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-15
Author(s):  
Zhong Jin ◽  
Yuqing Wang
Keyword(s):  
Nonlinear Equations ◽  
Numerical Experiments ◽  
Line Search ◽  
Filter Method ◽  
System Of Nonlinear Equations ◽  
Search Filter ◽  
Globally Convergent ◽  
Monotone Methods ◽  
Sufficient Reduction ◽  
New Iterative Method

We present a new iterative method based on the line search filter method with the nonmonotone strategy to solve the system of nonlinear equations. The equations are divided into two groups; some equations are treated as constraints and the others act as the objective function, and the two groups are just updated at the iterations where it is needed indeed. We employ the nonmonotone idea to the sufficient reduction conditions and filter technique which leads to a flexibility and acceptance behavior comparable to monotone methods. The new algorithm is shown to be globally convergent and numerical experiments demonstrate its effectiveness.

Solving System of Nonlinear Equations using Genetic Algorithm

2019 ◽  
Vol 10 (4) ◽  
pp. 877-886 ◽  
Author(s):  
Chhavi Mangla ◽  
Musheer Ahmad ◽  
Moin Uddin
Keyword(s):  
Genetic Algorithm ◽  
Nonlinear Equations ◽  
System Of Nonlinear Equations
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