The Research of Time-Delay Hyper-Chaotic Mapping Newton Iterative Method to Mechanism Synthesis

2009 ◽  
Author(s):  
Youxin Luo ◽  
Bin Zeng
Keyword(s):  
Time Delay ◽  
Iterative Method ◽  
Mechanism Synthesis ◽  
Chaotic Mapping ◽  
Newton Iterative Method

Two-Dimensional Hyper-Chaotic Mapping Interval Newton Iterative Method to Mechanism Synthesis

2011 ◽  
Vol 230-232 ◽  
pp. 764-768
Author(s):  
You Xin Luo ◽  
Bin Zeng
Keyword(s):  
Iterative Method ◽  
Discrete Systems ◽  
Initial Guess ◽  
Two Dimensional ◽  
Mechanism Synthesis ◽  
Krawczyk Operator ◽  
Chaotic Mapping ◽  
Newton Iterative Method ◽  
Approximate Synthesis ◽  
Chaos Sequences

Mechanism synthesis questions can be transformed into nonlinear equations to be found. Interval Newton iterative method is an important technique to one dimensional and multidimensional variables and iterative process exhibits sensitive dependence on initial guess point. The characteristic of hyper-chaotic sequences produced by two dimensional hyper-chaotic discrete systems was analyzed. Making use of the advantage of giving rigorous bounds for the exact solution, for the first time, combining hyper-chaos sequences and interval Newton iteration with Krawczyk operator, a new method to find all solutions was proposed. The numerical examples in linkage synthesis and approximate synthesis show that the method is correct and effective.

The Research of Two-Dimensional Probability Hyper-Chaotic Mapping Newton Iterative Method to Mechanism Synthesis

2010 ◽  
Vol 20-23 ◽  
pp. 670-675
Author(s):  
You Xin Luo ◽  
Bin Zeng
Keyword(s):  
Iterative Method ◽  
Discrete Systems ◽  
Initial Guess ◽  
Two Dimensional ◽  
Chaotic Mapping ◽  
Newton Iterative Method ◽  
All Solutions ◽  
Sensitive Dependence ◽  
Approximate Synthesis ◽  
First Time

Many questions in natural science and engineering are transformed into nonlinear equations to be found. Newton iterative method is an important technique to one dimensional and multidimensional variables and iterative process exhibits sensitive dependence on initial guess point. The probability characteristic of hyper-chaotic sequences produced by two dimensional hyper-chaotic discrete systems was analyzed. For the first time, a new method to find all solutions based on utilizing　two dimensional probability hyper-chaotic discrete mapping to obtain initial points to find all solutions of the nonlinear questions was proposed. The numerical examples in linkage synthesis and approximate synthesis show that the method is correct and effective.

Forward Displacement Analysis of 5SPS-1CCS Parallel Manipulator Based on Hyper-Chaotic Newton Method

2012 ◽  
Vol 507 ◽  
pp. 196-201
Author(s):  
You Xin Luo ◽  
Bin Zeng
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
Chaotic Mapping ◽  
Homotopy Continuation Method ◽  
Newton Iterative Method ◽  
Forward Displacement Analysis

Forward displacement analysis of parallel manipulators lead finally to solve the complex nonlinear equations, and its process is extremely difficult. The Newton iterative method is an important iterative technique for high-dimension nonlinear equations, but it is comparatively sensitive to initial value. To take chaos sequences as initial points of Newton iterative method, it can rapidly find all solutions of nonlinear equations. The novel approach of Newton iterative method based on parameter coupled hyper-chaotic mapping for solving nonlinear equations is presented. The mathematic model of the generalized 5SPS-1CCS parallel manipulator is created based on quaternion. A numerical example is given out, and its result is compared with the result of homotopy continuation method. The analysis results show that the new algorithm is simple, high efficiency, universal and can be used to forward displacement analysis of other coupled parallel manipulators.

scholarly journals Two solutions to Kirchhoff-type fourth-order implusive elastic beam equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Jian Liu ◽  
Wenguang Yu
Keyword(s):  
Iterative Method ◽  
Variational Methods ◽  
Critical Point ◽  
Fourth Order ◽  
Elastic Beam ◽  
Kirchhoff Type ◽  
Newton Iterative Method ◽  
Beam Equations ◽  
Critical Point Theorems ◽  
Elastic Beam Equations

AbstractIn this paper, the existence of two solutions for superlinear fourth-order impulsive elastic beam equations is obtained. We get two theorems via variational methods and corresponding two-critical-point theorems. Combining with the Newton-iterative method, an example is presented to illustrate the value of the obtained theorems.

Research on Newton Iterative Method and its Application in Locating Problem of Cameras

2010 ◽  
Vol 108-111 ◽  
pp. 112-116
Author(s):  
Ai Min Yang ◽  
Jin Cai Chang ◽  
Shao Hong Yan
Keyword(s):  
Iterative Method ◽  
Plane Surface ◽  
Target Surface ◽  
Newton Iterative Method ◽  
Limited Condition ◽  
Surface Length

According to the imagery coordinate’s mapping relation between the three points’(A,C,E) geometric limited condition on target surface ( length, perpendicular) and the image’s coordinate on the imagery plane surface to construct non- lineable equation models, we make use of the method of abstracting the center of a circle to get the coordinates of the three points 、 、 .In order to improve the precision and decrease the quantity of operation, we take the accelerateNewton Newton iterative method to evaluate the original numerical value by adding its repeating times to increase the precision of model, then to solve out the numerical value of coordinates of the three points A,C,E on the target’s surface, on the basis of this numerical value, we can fix the solution of the target’s surface’s equation. Try to assure the precision of the constructed model through these erroneous values, meanwhile, to make out the concrete analysis about the model’s stability.

scholarly journals Some novel Newton-type methods for solving nonlinear equations

2019 ◽  
Vol 38 (3) ◽  
pp. 111-123
Author(s):  
Morteza Bisheh-Niasar ◽  
Abbas Saadatmandi
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
Basins Of Attraction ◽  
Sixth Order ◽  
New Method ◽  
Order Convergence ◽  
Cubic Convergence ◽  
Numerical Examples ◽  
Newton Iterative Method

The aim of this paper is to present a new nonstandard Newton iterative method for solving nonlinear equations. The convergence of the proposed method is proved and it is shown that the new method has cubic convergence. Furthermore, two new multi-point methods with sixth-order convergence, based on the introduced method, are presented. Also, we describe the basins of attraction for these methods. Finally, some numerical examples are given to show the performance of our methods by comparing with some other methods available in the literature

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