Reconstruction of High Order Derivatives by New Mollification Methods
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摘要: 考虑由扰动数据重构原函数的导数问题.基于L-广义解正则化理论,提出了一个新的磨光方法的框架.给出一个具体的求解前3阶导数的算法,其中正则化策略选择了一种改进的TSVD(truncated singular value decomposition)方法(典则TSVD方法).数值结果进一步验证了理论结果及新方法的有效性.Abstract: The problem of reconstructing numerical derivatives from noisy data is considered. A new framework of mollification methods based on L-generalized solution regularization methods was proposed. A concrete algorithm for the first three derivatives was presented, in which a modification of TSVD (called cTSVD (canonical truncated singular value decomposition)) is chosen as the needed regularization technique. The numerical examples given verify the theoretical results and show the efficiency of the new method.
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