Parameter Optimization in the Regularized Shannon's Kernels of Higher-Order Discrete Singular Convolutions

• Main Authors: XIONG, Wei, ZHAO, Yibao, GU, Yun
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2003
• Subjects: Discrete singular convolutions; Energy minimization; Numerical differentiators; Objective functions; Parameter optimization; Regularized Shannon's kernels; Physical Sciences and Mathematics
• Online Access: https://ink.library.smu.edu.sg/lkcsb_research/929; https://ink.library.smu.edu.sg/context/lkcsb_research/article/1928/viewcontent/Parameter_optimization_Shannon_2003.pdf
• Institution: Singapore Management University

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.