China 
Africa 
Explore chapters and articles related to this topic
Approximation Theory
Published in Azmy S. Ackleh, Edward James Allen, Ralph Baker Kearfott, Padmanabhan Seshaiyer, Classical and Modern Numerical Analysis, 2009
Azmy S. Ackleh, Edward James Allen, Ralph Baker Kearfott, Padmanabhan Seshaiyer
Trigonometric interpolation is often useful for interpolation of large amounts of data when the data are given at equally spaced points. In the trigonometric interpolation problem, we have N values of f(x) on the interval [0,2π] at equally spaced points xj=2πj/N,j=0,1,…,N−1, i.e., x0,fx0, x1,fx1,…,xN−1,fxN−1, where f(0)=f(2π), i.e., f is periodic with period 2π. We wish to find the trigonometric polynomial p(x)=∑j=0N−1cjeijx
Denoising for satellite laser altimetry full-waveform data based on EMD-Hurst analysis
Published in International Journal of Digital Earth, 2020
Zhijie Zhang, Huan Xie, Xiaohua Tong, Hanwei Zhang, Yang Liu, Binbin Li
Although the EMD decomposition algorithm shows an outstanding performance in the processing of non-linear and non-stationary signals, the algorithm itself has some weaknesses, such as end effects, the scale mixing problem, the sifting stop criteria setting for identifying IMFs, and the envelope interpolation method (Hawley, Atlas, and Chizeck 2010; Lei et al. 2013), therefore, in different applications, the parameters that EMD algorithm relies on and will affect the decomposition accuracy need to be selected cautiously. For example, comparing with cubic spline interpolation, linear or polynomial method will increase the number of iterations and generate over-decomposition signals which are dispersed in adjacent IMFs, and other methods like trigonometric interpolation cosine interpolation have been used to obtain an improved decomposition (Roy and Doherty 2011). Moreover, it is impossible for the end of the signal to be at the maximum or minimum at the same time, so the upper and lower envelopes will diverge at both ends of the data sequence, and this divergence will gradually inward as the operation proceeds, thus affecting the whole data sequence. This is the end effect. To eliminate the end effects included in IMFs, various methods to extend the length of a signal have been put forward (Yang et al. 2008; He, Shen, and Wang 2012). Regarding the sifting stop criterion, terminating the iteration process with an excessively low threshold can lead to problems such as those mentioned earlier (excessive decomposition of iterations). A bandwidth criterion can be an improved method for the original EMD criterion (Xie et al. 2008).
Harmonic interpolation of Hermite type based on Radon projections with constant distances
Published in Applicable Analysis, 2019
We can use Theorem 1.7 in [16, Chapter X] to show that , since it is the determinant of the coefficient matrix of the trigonometric interpolation problem. But we need the continuity and boundedness as in Lemma 3.4 to prove our main results. On the other hand, applying the factorization theorem in [12] to we can write where is a certain determinant whose elements are divided differences. The fact that is not trivial. Moreover the estimate in Lemma 3.4 cannot be deduced from Equation (9).
The factorization method to reconstruct a combination of penetrable obstacle and arc
Published in Applicable Analysis, 2022
Select 64 incident directions , , for each incident direction we measure the far field pattern in the directions , using the trigonometric interpolation and collocation method introduced in [27] and add random noise α to each . This gives our set of data , which we collect in a matrix which is the discretized version of the far field operator F.