Exact Incremental Learning for a Single Non-linear Neuron Based on Taylor Expansion and Greville Formula

Author(s):  
David Martínez-Rego ◽  
Oscar Fontenla-Romero ◽  
Amparo Alonso-Betanzos
2014 ◽  
Vol 8 ◽  
Author(s):  
Arjan Gijsberts ◽  
Rashida Bohra ◽  
David Sierra González ◽  
Alexander Werner ◽  
Markus Nowak ◽  
...  

2014 ◽  
Vol 59 (05) ◽  
pp. 1450045 ◽  
Author(s):  
SHEUE LI ONG ◽  
CHONG MUN HO

The untested assumption of linear relationship between stocks and bonds in previous empirical studies may lead to an invalid conclusion if the actual relationship is non-linear. The emphasis of this paper is on the effect of non-linearities on causal relationships between stocks and bonds in the cases of Malaysia and Singapore. Results from linearity tests indicate the existence of non-linearities in the dynamic relationship between stocks and bonds. Non-linear causality test results based on Taylor expansion suggest that non-linear causality flows from stocks to bonds and vice versa. The test further confirms that bonds with different maturity dates have different relationships with stocks.


2017 ◽  
Vol 21 (2) ◽  
pp. 813-817 ◽  
Author(s):  
Guo-Cheng Wu ◽  
Dumitru Baleanu ◽  
Wei-Hua Luo

A time-fractional non-linear diffusion equation of two orders is considered to investigate strong non-linearity through porous media. An equivalent integral equation is established and Adomian polynomials are adopted to linearize non-linear terms. With the Taylor expansion of fractional order, recurrence formulae are proposed and novel numerical solutions are obtained to depict the diffusion behaviors more accurately. The result shows that the method is suitable for numerical simulation of the fractional diffusion equations of multi-orders.


2020 ◽  
Vol 4 (2) ◽  
pp. 6-8
Author(s):  
Narmeen N. Nadir

In this paper, Taylor expansion has been used for solving non-linear Volterra integral equations (VIEs) of the second kind. This method allows us to overcome the difficulty caused by integrals and non-linearity; also, it has more precise and rapidly convergent to the exact solution. Two examples are presented for illustrate the performance of this method.


2019 ◽  
Vol 6 (2) ◽  
pp. 170-180
Author(s):  
Agus Suprianto ◽  
Wahyudi Wahyudi ◽  
Wiwit Suryanto ◽  
Ari Setiawan ◽  
Aryono Adhi ◽  
...  

The mathematical modelling of geological structures, i.e. magma intrusion or dyke, has been done,  based on magnetic data with inversion techniques using MatLab. The magnetic equation is a non-linear equation, and completion is done using a linear approach to non-linear mathematical models of magnetic data using the Taylor expansion approach and Jacobi Matrix. The first step of this research is to make synthetic data forward modelling from the magnetic equation of magma intrusion or dyke cases without errors, and the next stepping then add errors to the data. The next step is to do an inversion to get the parameters sought, i.e. depth and angle of the magma intrusion, by giving initial guesses, and then re-correct iteratively until convergent results are obtained. Finally, parameters of slope dyke or thin magma intrusion and its depth can be determined. The results obtained indicate that this technique can be used to get physical parameters sought from magnetic data for simple geological cases, i.e. dyke and magma intrusion.


1967 ◽  
Vol 28 ◽  
pp. 105-176
Author(s):  
Robert F. Christy

(Ed. note: The custom in these Symposia has been to have a summary-introductory presentation which lasts about 1 to 1.5 hours, during which discussion from the floor is minor and usually directed at technical clarification. The remainder of the session is then devoted to discussion of the whole subject, oriented around the summary-introduction. The preceding session, I-A, at Nice, followed this pattern. Christy suggested that we might experiment in his presentation with a much more informal approach, allowing considerable discussion of the points raised in the summary-introduction during its presentation, with perhaps the entire morning spent in this way, reserving the afternoon session for discussion only. At Varenna, in the Fourth Symposium, several of the summaryintroductory papers presented from the astronomical viewpoint had been so full of concepts unfamiliar to a number of the aerodynamicists-physicists present, that a major part of the following discussion session had been devoted to simply clarifying concepts and then repeating a considerable amount of what had been summarized. So, always looking for alternatives which help to increase the understanding between the different disciplines by introducing clarification of concept as expeditiously as possible, we tried Christy's suggestion. Thus you will find the pattern of the following different from that in session I-A. I am much indebted to Christy for extensive collaboration in editing the resulting combined presentation and discussion. As always, however, I have taken upon myself the responsibility for the final editing, and so all shortcomings are on my head.)


Optimization ◽  
1975 ◽  
Vol 6 (4) ◽  
pp. 549-559
Author(s):  
L. Gerencsér

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