Bloch-McConnell方程参数反演问题矩阵指数算法  

The Method of Matrix Exponential in Inverse Problem of Bloch-McConnell Equation

作　　者：肖刚[1] 肖红[1] 

机构地区：[1]韩山师范学院数学与统计学院,广东潮州521041

出　　处：《科技通报》2015年第9期5-7,共3页Bulletin of Science and Technology

基　　金：国家自然科学基金重点项目(No.30930027);广东省自然科学基金项目(No.S013010013372)

摘　　要：针对时变Bloch-Mc Connell方程的参数识别反问题,利用矩阵指数给出方程近似解。在此基础上,应用非线性优化算法对其参数进行反演,讨论数据扰动和初值选取不同时对反演结果的影响,验证所提出的方法具有较高的精度和速度。最后,把算法推广到微分方程组具有矩阵指数解的反演问题。In view of time-varying Bloch-McConnell equation of the inverse problem in parameter estimation, an approximate solution with matrix exponential is given. On this basis, a nonlinear optimization algorithm is used to estimate the parameters, and the results are discussed with the data perturbation and initial value selection, at the same time to verify the effectiveness of the proposed method has high accuracy and speed. Finally, the algorithm is extend to the inverse problem of the differential equations with matrix exponential solution.

关 键 词：Bloch-McConnell方程 参数反演 微分方程 矩阵指数 MATLAB 

分 类 号：O241.82[理学—计算数学]