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Title: Parameter optimization in the regularized Shannon's kernels of higher-order discrete singular convolutions
Authors: Xiong, W.
Zhao, Y. 
Gu, Y.
Keywords: Discrete singular convolutions
Energy minimization
Numerical differentiators
Objective functions
Parameter optimization
Regularized Shannon's kernels
Issue Date: May-2003
Citation: Xiong, W., Zhao, Y., Gu, Y. (2003-05). Parameter optimization in the regularized Shannon's kernels of higher-order discrete singular convolutions. Communications in Numerical Methods in Engineering 19 (5) : 377-386. ScholarBank@NUS Repository.
Abstract: The δ-type discrete singular convolution (DSC) algorithm has recently been proposed and applied to solve kinds of partial differential equations (PDEs). With appropriate parameters, particularly the key parameter r in its regularized Shannon's kernel, the DSC algorithm can be more accurate than the pseudospectral method. However, it was previously selected empirically or under constrained inequalities without optimization. In this paper, we present a new energy-minimization method to optimize r for higher-order DSC algorithms. Objective functions are proposed for the DSC algorithm for numerical differentiators of any differential order with any discrete convolution width. Typical optimal parameters are also shown. The validity of the proposed method as well as the resulted optimal parameters have been verified by extensive examples. © 2003 John Wiley and Sons, Ltd.
Source Title: Communications in Numerical Methods in Engineering
ISSN: 10698299
DOI: 10.1002/cnm.596
Appears in Collections:Staff Publications

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