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

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.