微分方程反问题的梯度正则化法

本文在微分方程反问题研究当前发展状况的基础上,提出了一种求解微分方程反问题的比较统一的方法——梯度正则化法。该方法将反问题的求解分为两个主要部分,一是展开以求补充条件对未知参数的梯度矩阵,二是正则化以解不适定的线性方程组。梯度正则化法从反问题的共性入手,未附加任何特殊的约束,所以可以适用各种类型的反问题,且在求解时不受空间维数的限制。

Gradient-Regularization Method to Solve the Inverse Problems of Differential Equation

On the basis of previous works, here we propose a general approach tosolve the inverse problems of differential equation--Gradient-Regularizationmethod. Using the GR method, we consider the inverse problems from two aspects, one is how to get the gradient matrix of supplementary conditions to unkown parameters, another is how to solve the Ill-posed linear algebraic equations. The GR method has considered the generality of inverse problems and no special constriants is added. So it can be used to solve various kinds of inverse problems.