Zhenyu Zhao

Zhenyu Zhao
Guangdong Ocean University · College of Science

About

19
Publications
1,328
Reads
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92
Citations
Citations since 2017
5 Research Items
66 Citations
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2017201820192020202120222023051015
2017201820192020202120222023051015
2017201820192020202120222023051015

Publications

Publications (19)
Article
Full-text available
In this paper, a Cauchy problem for the Laplace equation is considered. We develop a modified Tikhonov regularization method based on Hermite expansion to deal with the ill posed-ness of the problem. The regularization parameter is determined by a discrepancy principle. For various smoothness conditions, the solution process of the method is unifor...
Article
Based 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 periodic function on a larger domain. The Tikhonov regularization method in Hilbert scales is presented to deal with the ill-posedness of the problem. The Sobolev norm...
Article
Full-text available
In this paper, we further extend the Filon-type method to the Bessel function expansion for calculating Fourier integral. By means of complex analysis, this expansion is effective for all the oscillation frequencies. Namely, the errors of the expansion not only decrease as the order of the derivative increases, but also decrease rapidly as the freq...
Article
This paper develops a new method to deal with the problem of identifying the unknown source in the Poisson equation. We obtain the regularization solution by the Tikhonov regularization method with a super-order penalty term. The order optimal error bounds can be obtained for various smooth conditions when we choose the regularization parameter by...
Article
Full-text available
A modified truncated singular value decomposition method for solving ill-posed problems is presented in this paper, in which the solution has a slightly different form. Both theoretical and numerical results show that the limitations of the classical TSVD method have been overcome by the new method and very few additive computations are needed.
Article
In this paper, we consider the problem for identifying the unknown source in the Poisson equation. The Tikhonov regularization method in Hilbert scales is extended to deal with illposedness of the problem and error estimates are obtained with an a priori strategy and an a posteriori choice rule to find the regularization parameter. The user does no...
Article
Full-text available
In this paper, we consider the problem for determining an unknown source in the heat equation. The Tikhonov regularization method in Hilbert scales is presented to deal with ill-posedness of the problem and error estimates are obtained with a posteriori choice rule to find the regularization parameter. The smoothness parameter and the a priori boun...
Article
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 cor...
Article
In this article, a backward heat conduction problem is considered. A modified Tikhonov regularization method is presented and error estimates are obtained with an a priori strategy and an a posteriori choice rule to find the regularization parameter. Numerical tests show that the proposed method is effective and stable.
Article
Full-text available
A numerical differentiation problem for a given function with noisy data is discussed in this paper. A Legendre-Gauss-Lobatto interpolation method with a truncated strategy has been introduced to deal with ill-posed ness. The theoretical analysis and numerical results show that the method is effective.
Article
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 serie...
Article
In this paper, we present a Newton-type method with double regularization parameters for nonlinear ill-pose problems. The key step in the process that a reasonable choice rule to determine these two regularization parameters is presented. And the convergence and the stability of the method are discussed. Numerical experiment shows the effectiveness...
Article
In this paper we consider the numerical differentiation of functions specified by noisy data. A new approach, which is based on an integral equation of the first kind with a suitable compact operator, is presented and discussed. Since the singular system of the compact operator can be obtained easily, TSVD is chosen as the needed regularization tec...
Conference Paper
A numerical differentiation problem for a given function with noisy data is discussed in this paper. A truncated Chebyshev spectral method has been introduced to deal with the ill-posedness of the problem. The numerical results shows that the method is very effective.
Conference Paper
Full-text available
In this paper, we present a new method for numerical differentiation of bivariate periodic functions when a set of noisy data is given. TSVDis chosen as the needed regularization technique. It turns out the new method coincides with some type of truncated Fourier series approach. A numerical example is also given to show the efficiency of themethod...

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