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

DOI：10.3770/j.issn:2095-2651.2017.01.007

 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

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.

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.