Chongjun LI,Linlin XIE,Haidong LI.Reconstruction of the Linear Ordinary Differential System Based on Discrete Points[J].数学研究及应用,2017,37(1):73~89
Reconstruction of the Linear Ordinary Differential System Based on Discrete Points
Reconstruction of the Linear Ordinary Differential System Based on Discrete Points
投稿时间:2016-11-23  最后修改时间:2016-12-19
DOI:10.3770/j.issn:2095-2651.2017.01.007
中文关键词:  differential system  discrete data  normal vector method  least square method  parameterization
英文关键词:differential system  discrete data  normal vector method  least square method  parameterization
基金项目:Supported by the National Natural Science Foundation of China (Grant Nos.11290143; 11471066; 11572081), the Fundamental Research of Civil Aircraft (Grant No.MJF-2012-04) and the Fundamental Research Funds for the Central Universities (Grant No.DUT15LK44).
作者单位
Chongjun LI School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China 
Linlin XIE School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China 
Haidong LI School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China 
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中文摘要:
      In this paper, we discuss an inverse problem, i.e., the reconstruction of a linear differential dynamic system from the given discrete data of the solution. We propose a model and a corresponding algorithm to recover the coefficient matrix of the differential system based on the normal vectors from the given discrete points, in order to avoid the problem of parameterization in curve fitting and approximation. We also give some theoretical analysis on our algorithm. When the data points are taken from the solution curve and the set composed of these data points is not degenerate, the coefficient matrix $A$ reconstructed by our algorithm is unique from the given discrete and noisefree data. We discuss the error bounds for the approximate coefficient matrix and the solution which are reconstructed by our algorithm. Numerical examples demonstrate the effectiveness of the algorithm.
英文摘要:
      In this paper, we discuss an inverse problem, i.e., the reconstruction of a linear differential dynamic system from the given discrete data of the solution. We propose a model and a corresponding algorithm to recover the coefficient matrix of the differential system based on the normal vectors from the given discrete points, in order to avoid the problem of parameterization in curve fitting and approximation. We also give some theoretical analysis on our algorithm. When the data points are taken from the solution curve and the set composed of these data points is not degenerate, the coefficient matrix $A$ reconstructed by our algorithm is unique from the given discrete and noisefree data. We discuss the error bounds for the approximate coefficient matrix and the solution which are reconstructed by our algorithm. Numerical examples demonstrate the effectiveness of the algorithm.
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