2D weight function development using a complex Taylor series expansion method

2012 ◽  
Vol 86 ◽  
pp. 23-37 ◽  
Author(s):  
David Wagner ◽  
Harry Millwater
Keyword(s):  
Weight Function ◽  
Series Expansion ◽  
Taylor Series ◽  
Taylor Series Expansion ◽  
Expansion Method ◽  
Series Expansion Method

Rationalize the irrational and fractional expressions in nonlinear analysis

2016 ◽  
Vol 30 (04) ◽  
pp. 1650068 ◽  
Author(s):  
Yongfeng Yang ◽  
Tingdong Jiang ◽  
Zhong Ren ◽  
Junyao Zhao ◽  
Zheng Zhang
Keyword(s):  
Nonlinear Analysis ◽  
Series Expansion ◽  
Taylor Series ◽  
Impact Force ◽  
Taylor Series Expansion ◽  
Expansion Method ◽  
Stochastic Bifurcation ◽  
Bifurcation And Chaos ◽  
Integral Process ◽  
Series Expansion Method

Chebyshev polynomial approximation is an effective method to study the stochastic bifurcation and chaos. However, due to irrational and fractional expressions existing in the denominator of some mechanical systems, the integral process is very complicated. The Taylor series expansion is proposed to expand the irrational and fractional expressions into a series of polynomials. Smooth and discontinuous oscillator was taken as an example, and the results show that the Taylor series expansion method is acceptable. The rub-impact force was taken as another example. Numerical results indicate that the method is suitable for the rub-impact rotor system.

A novel method for computing the vertical gradients of the potential field: Application to downward continuation

2019 ◽  
Author(s):  
Kha Van Tran ◽  
Trung Nhu Nguyen
Keyword(s):  
Series Expansion ◽  
Taylor Series ◽  
Potential Field ◽  
Continuation Method ◽  
Taylor Series Expansion ◽  
Expansion Method ◽  
Downward Continuation ◽  
Source Distribution ◽  
Vertical Derivative ◽  
Series Expansion Method

Summary Downward continuation is a very useful technique in the interpretation of potential field data. It would enhance the short wavelength of the gravity anomalies or accentuate the details of the source distribution. Taylor series expansion method has been proposed to be one of the best downward continued methods. However, the method using high-order vertical derivatives leads to low accuracy and instability results in many cases. In this paper, we propose a new method using a combination of Taylor series expansion and upward continuation for computing vertical derivatives. This method has been tested on the gravitational anomaly of infinite horizontal cylinder in both cases with and without random noise for higher accurate and stable than Hilbert transform method and Laplace equation method, especially in the case of noise input data. This vertical derivative method is applied successfully to calculate the downward continuation according to Taylor series expansion method. The downward continuation is also tested on both complex synthetic models and real data in the East Vietnam Sea (South China Sea). The results reveal that by calculating this new vertical derivative, the downward continuation method gave higher accurate and stable than the previous downward continuation methods.

RFID Localization Algorithm Based on Taylor Series Expansion

2013 ◽  
Vol 756-759 ◽  
pp. 3501-3505 ◽  
Author(s):  
You Liang Yang ◽  
Jing Zhang ◽  
Fan Wei Meng ◽  
Cui Hong Ma
Keyword(s):  
Series Expansion ◽  
Taylor Series ◽  
Nearest Neighbor ◽  
Taylor Series Expansion ◽  
Expansion Method ◽  
Indoor Positioning ◽  
Localization Algorithm ◽  
Data Correlation ◽  
Correlation Algorithm ◽  
Series Expansion Method

RFID is widely used in indoor positioning, as one of the typical system LANDMARK introduced reference label, used the nearest neighbor data correlation algorithm. This article uses the Taylor series expansion method, by the LANDMARK law get positioning results for further processing, resulting in more accurate positioning results.

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