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 ...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.展开更多
基金Supported by the National Natural Science Foundation of China(Grant Nos.1129014311471066+2 种基金11572081)the Fundamental Research of Civil Aircraft(Grant No.MJF-2012-04)the Fundamental Research Funds for the Central Universities(Grant No.DUT15LK44)
文摘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.
