The Experts below are selected from a list of 288 Experts worldwide ranked by ideXlab platform
Zhenyu Zhao - One of the best experts on this subject based on the ideXlab platform.
-
Numerical Differentiation for two-dimensional functions by a Fourier extension method
Inverse Problems in Science and Engineering, 2019Co-Authors: Zehong Meng, Zhenyu Zhao, Duan Mei, Yongxiong ZhouAbstract:ABSTRACTBased on the idea of Fourier extension, we develop a new method for Numerical Differentiation of two-dimensional functions on an arbitrary domain. The function will be extended to a periodi...
-
A stabilized algorithm for multi-dimensional Numerical Differentiation
Journal of Algorithms & Computational Technology, 2016Co-Authors: Zhenyu Zhao, Zehong Meng, Liang Zhao, Lei You, Ou XieAbstract:We develop a multi-dimensional Numerical Differentiation method in this paper. To obtain stable Numerical derivatives, the Tikhonov regularization method in Hilbert scales is proposed to deal with ...
-
Hermite spectral and pseudospectral methods for Numerical Differentiation
Applied Numerical Mathematics, 2011Co-Authors: Zhenyu Zhao, Junfeng LiuAbstract:A Numerical Differentiation problem for a given function with noisy data is discussed in this paper. A mollification method based on spanned by Hermite functions is proposed and the mollification parameter is chosen by a discrepancy principle. The convergence estimates of the derivatives are obtained. To get a practical approach, we also derive corresponding results for pseudospectral (Hermite-Gauss interpolation) approximations. Numerical examples are given to show the efficiency of the method.
-
a truncated legendre spectral method for solving Numerical Differentiation
International Journal of Computer Mathematics, 2010Co-Authors: Zhenyu ZhaoAbstract:A Numerical Differentiation problem for a given function with noisy data is discussed in this paper. A truncated spectral method has been introduced to deal with the ill-posedness of the problem. The theoretical analysis shows that the smoother the genuine solution, the higher the convergence rate of the Numerical solution by our method. Numerical examples are also given to show the efficiency of the method.
-
Numerical Differentiation for periodic functions
Inverse Problems in Science and Engineering, 2010Co-Authors: Zhenyu Zhao, Zehong MengAbstract:In this article we consider the Numerical Differentiation of periodic functions specified by noisy data. A new method, which is based on the truncated singular value decomposition (TSVD) regularization technique of a suitable compact operator, is presented and analysed. It turns out the new method coincides with some type of truncated Fourier series approach. Numerical examples are also given to show the efficiency of the method.
François Dubeau - One of the best experts on this subject based on the ideXlab platform.
-
Standard and Corrected Numerical Differentiation Formulae
Communications in Advanced Mathematical Sciences, 2019Co-Authors: François DubeauAbstract:Standard Numerical Differentiation rules that might be established by the method of undetermined coefficients are revisited. Best truncation error bounds are established by a direct method and by the method of integration by parts "backwards". A new method to increase the order of the truncation error using a primitive is presented. This approach leads to corrected Numerical Differentiation rules. Differentiation formulae and Numerical tests are presented.
-
A remark on Richardson's extrapolation process and Numerical Differentiation formulae
Journal of Computational Physics: X, 2019Co-Authors: François DubeauAbstract:Abstract Richardson's extrapolation process is a well known method to improve the order of several approximation processes. Here we observe that for Numerical Differentiation, Richardson's process can be applied not only to improve the order of a Numerical Differentiation formula but also to find in fact the original formula.
Woo Young Choi - One of the best experts on this subject based on the ideXlab platform.
-
A new method for stable Numerical Differentiation
Current Applied Physics, 2009Co-Authors: Woo Young ChoiAbstract:Abstract In this paper, we proposed a new algorithm for stable Numerical Differentiation by optimizing node intervals. With the algorithm, noise-free differentiated values can be extracted within one-percent error. By overcoming noise problem due to Numerical Differentiation process, our algorithm can easily extract the differentiated values. Also, it can be extended to high order Differentiation. To confirm the proposed algorithm, we applied it to the analysis of MOSFET electrical characteristics. It will provide us with a useful analysis tool in the field of parameter extraction from Numerical data such as device characterization.
B Pasikduncan - One of the best experts on this subject based on the ideXlab platform.
-
Numerical Differentiation and parameter estimation in higher order linear stochastic systems
IEEE Transactions on Automatic Control, 1996Co-Authors: T E Duncan, Petr Mandl, B PasikduncanAbstract:For a linear time-invariant system of order d/spl ges/2 with a white noise disturbance, the input and the output are assumed to be sampled at regular time intervals. Using only these observations, some approximate values of the first d-1 derivatives are obtained by a Numerical Differentiation scheme, and the unknown system parameters are estimated by a discretization of the continuous-time least-squares formulas. These parameter estimates have an error which does not approach zero as the sampling interval approaches zero. This asymptotic error is shown to be associated with the inconsistency of the quadratic variation estimate of the white noise local variance based on the sampled observations. The use of an explicit correction term in the least-squares estimates or the use of some special Numerical Differentiation formulas eliminates the error in the estimates.
Zhi Qian - One of the best experts on this subject based on the ideXlab platform.
-
Wavelets and high order Numerical Differentiation
Applied Mathematical Modelling, 2010Co-Authors: Xiao-li Feng, Zhi QianAbstract:Abstract Numerical Differentiation is a classical ill-posed problem. In this paper, a wavelet regularization method for high order Numerical derivatives is given and an order optimal Holder-type stability estimate is also provided. Some Numerical examples show that the method is very effective.
