椭圆方程柯西问题磨光正则化参数的后验选取

A posteriori choice rule for the mollification regularization parameter for the Cauchy problem of an elliptic equation

通过将带有参数的Gaussian函数和测量数据作卷积,把不适定问题转化为适定问题进行求解,给出基于Morozov偏差原理的后验参数选取规则并得到了精确解和正则近似解之间的误差估计。数值实验表明了磨光正则化后验参数选取规则的有效性。

We transform the ill-posed problem into a well-posed problem by convolutioning the Gaussian function with parameters and the measurement data. A posteriori parameter choice rule is given which is based on Morozov＇s discrepancy principle and the er- ror estimates between the exact solution and its approximation are also given. Numerical experiments show the validity of mollifica- tion regularization posteriori parameter choice rule.