Two Modified Newton-Raphson Iteration Algorithms for Yang-Baxter-like Matrix Equation with Step-Size Analyses

2020 ◽  
Author(s):  
Guancheng Wang ◽  
Donghui Li ◽  
Xiangyi Chen ◽  
Haoen Huang
Keyword(s):  
Matrix Equation ◽  
Step Size ◽  
Newton Raphson ◽  
Raphson Iteration

Neural Dynamics and Newton–Raphson Iteration for Nonlinear Optimization

2014 ◽  
Vol 9 (2) ◽  
Author(s):  
Dongsheng Guo ◽  
Yunong Zhang
Keyword(s):  
Nonlinear Optimization ◽  
Optimization Problems ◽  
Activation Function ◽  
Neural Dynamics ◽  
Time Varying ◽  
Step Size ◽  
Gradient Based ◽  
Digital Hardware ◽  
Newton Raphson ◽  
Raphson Iteration

In this paper, a special type of neural dynamics (ND) is generalized and investigated for time-varying and static scalar-valued nonlinear optimization. In addition, for comparative purpose, the gradient-based neural dynamics (or termed gradient dynamics (GD)) is studied for nonlinear optimization. Moreover, for possible digital hardware realization, discrete-time ND (DTND) models are developed. With the linear activation function used and with the step size being 1, the DTND model reduces to Newton–Raphson iteration (NRI) for solving the static nonlinear optimization problems. That is, the well-known NRI method can be viewed as a special case of the DTND model. Besides, the geometric representation of the ND models is given for time-varying nonlinear optimization. Numerical results demonstrate the efficacy and advantages of the proposed ND models for time-varying and static nonlinear optimization.

scholarly journals Estimation of the Extreme Distribution Model of Economic Losses Due to Outbreaks Using the POT Method with Newton Raphson Iteration

2021 ◽  
Vol 2 (1) ◽  
pp. 37-45
Author(s):  
Riza Adrian Ibrahim ◽  
Sukono Sukono ◽  
Riaman Riaman
Keyword(s):  
Estimation Method ◽  
Random Variable ◽  
Value Theory ◽  
Extreme Value ◽  
Distribution Model ◽  
Economic Losses ◽  
Extreme Distribution ◽  
Newton Raphson ◽  
The Government ◽  
Raphson Iteration

Extreme distribution is the distribution of a random variable that focuses on determining the probability of small values in the tail areaof the distribution. This distribution is widely used in various fields, one of which is reinsurance. An outbreak catastrophe is non-natural disaster that can pose an extreme risk of economic loss to a country that is exposed to it. To anticipate this risk, the government of a country can insure it to a reinsurance company which is then linkedto bonds in the capital market so that new securities are issued, namely outbreakcatastrophe bonds. In pricing, knowledge of the extreme distribution of economic losses due to outbreak catastrophe is indispensable. Therefore, this study aims to determine the extreme distribution model of economic losses due to outbreak catastrophe whose models will be determined by the approaches and methods of Extreme Value Theory and Peaks Over Threshold, respectively. The threshold value parameter of the model will be estimated by Kurtosis Method, while the other parameters will be estimated with Maximum Likelihood Estimation Method based on Newton-Raphson Iteration. The result of the research obtained is the resulting model of extreme value distribution of economic losses due to outbreak catastrophe that can be used by reinsurance companies as a tool in determining the value of risk in the outbreak catastrophe bonds.

A Dyad Search Algorithm for Solving Planar Linkages Using the Dyad Method

1992 ◽  
Author(s):  
Lofti Romdhane
Keyword(s):  
Search Algorithm ◽  
Class Ii ◽  
Graph Representation ◽  
Step Size ◽  
Lower Pair ◽  
Fast Solution ◽  
Complete Automation ◽  
Newton Raphson ◽  
Dyad Analysis ◽  
Planar Linkages

Abstract Based on graph representation of planar linkages, a new algorithm was developed to identify the different dyads of a mechanism. A dyad or class II group, is composed of two binary links connected by either a revolute (1) or a slider (0) pair with provision for attachment to other links by lower pair connectors located at the end of each link. There are five types of dyads: the D111, D101, D011, D001, and D010. The dyad analysis of a mechanism is predicated on the ability to construct the system from one or more of the five binary structure groups or class II groups. If the mechanism is complicated and several dyads are involved, the task of identifying these dyads by inspection could be difficult and time consuming for the user. This algorithm allows a complete automation of this task. This algorithm is based on the Dijkstra’s algorithm, for finding the shortest path in a graph, and it is used to develop a computer program, called KAMEL: Kinematic Analysis of MEchanical Linkages, and implemented on an IBM-PC PS/2 model 80. When compared to algorithmic methods, like the Newton-Raphson, the dyad method proved to be a very efficient one and requires as little as one tenth of the time needed by the method using Newton-Raphson algorithm. Moreover, the dyad method yields the exact solution of the position analysis and no initial estimates are needed to start the analysis. This method is also insensitive to the value of the step-size crank rotation, therefore, allowing a very accurate and fast solution of the mechanism at any position of the input link.

New methods for projecting a 3D object onto a free-form surface

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Jingyu Pei ◽  
Xiaoping Wang ◽  
Leen Zhang ◽  
Yu Zhou ◽  
Jinyuan Qian
Keyword(s):  
Approximate Solution ◽  
New Method ◽  
Free Form ◽  
Parallel Projection ◽  
Content Type ◽  
3D Object ◽  
New Methods ◽  
Free Form Surface ◽  
Newton Raphson ◽  
Raphson Iteration

Purpose This paper aims to provide a series of new methods for projecting a three-dimensional (3D) object onto a free-form surface. The projection algorithms presented can be divided into three types, namely, orthogonal, perspective and parallel projection. Design/methodology/approach For parametric surfaces, the computing strategy of the algorithm is to obtain an approximate solution by using a geometric algorithm, then improve the accuracy of the approximate solution using the Newton–Raphson iteration. For perspective projection and parallel projection on an implicit surface, the strategy replaces Newton–Raphson iteration by multi-segment tracing. The implementation takes two mesh objects as an example of calculating an image projected onto parametric and implicit surfaces. Moreover, a comparison is made for orthogonal projections with Hu’s and Liu’s methods. Findings The results show that the new method can solve the 3D objects projection problem in an effective manner. For orthogonal projection, the time taken by the new method is substantially less than that required for Hu’s method. The new method is also more accurate and faster than Liu’s approach, particularly when the 3D object has a large number of points. Originality/value The algorithms presented in this paper can be applied in many industrial applications such as computer aided design, computer graphics and computer vision.

scholarly journals Calculation of Flight Data Fusion Coefficients Using Newton–Raphson Iterations

2020 ◽  
pp. 100-103
Author(s):  
Elkhan Nariman Sabziev
Keyword(s):  
Differential Equations ◽  
Data Fusion ◽  
Boundary Value Problem ◽  
Iteration Method ◽  
Measurement Errors ◽  
Continuous Model ◽  
System Of Differential Equations ◽  
Flight Data ◽  
Newton Raphson ◽  
Raphson Iteration

The problem of plotting the flight path of an aircraft based on flight data containing numerous measurement errors is investigated. A theoretical (continuous) model of the flight data fusion problem is proposed in the form of a boundary value problem for a system of differential equations with unknown coefficients. The application of the Newton–Raphson iteration method for calculating the sought-for coefficients is described.

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