A noise-suppressing Newton-Raphson iteration algorithm for solving the time-varying Lyapunov equation and robotic tracking problems

2021 ◽  
Vol 550 ◽  
pp. 239-251
Author(s):  
Guancheng Wang ◽  
Haoen Huang ◽  
Limei Shi ◽  
Chuhong Wang ◽  
Dongyang Fu ◽  
...  
Keyword(s):  
Lyapunov Equation ◽  
Iteration Algorithm ◽  
Time Varying ◽  
Robotic Tracking ◽  
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 Aspect Ratio of Slender Web & Postbuckling Behaviour / Pomer Strán Štíhlej Steny A Pokritické Pôsobenie

2012 ◽  
Vol 12 (2) ◽  
pp. 153-160
Author(s):  
Martin Psotný
Keyword(s):  
Variational Principle ◽  
Aspect Ratio ◽  
Total Potential Energy ◽  
Iteration Algorithm ◽  
Initial Imperfections ◽  
Total Potential ◽  
Non Linear ◽  
Newton Raphson ◽  
Raphson Iteration ◽  
The Web

Abstract Postbuckling analysis of slender web loaded in compression is presented. The non-linear FEM equations [14] are derived from the variational principle of minimum of total potential energy [13]. To obtain the non-linear equilibrium paths, Newton-Raphson iteration algorithm [11], [12] is used. Peculiarities of the effect of the initial imperfections [7], [8] on load-deflection paths are investigated with respect to aspect ratio of the web. Special attention is focused on the postbuckling mode of the web.

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.

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