求线性不适定方程L-广义解的隐式迭代法

An Implicit Iterative Method for L-Generalized Solution of Linear Ill-Posed Equations

本文首先指出可以把求不适定算子方程的 L-广义解归结为求另一个方程的 Moore-Penrose广义解 ,然后把隐式迭代法推广应用于求 L -广义解 .文中还考虑了离散方法 ,给出了数值例子 ,最后用例子说明了确定 L

We first point out that the L generalized solution of a linear ill posed equation can be reduced to the Moore Penrose generalized solution of another ill posed equation, and thus may apply the implicit iterative method to finding L generalized solution. A discretization method is discussed in the paper and numerical examples are also given. Finally, the authors indicate by an example how to determine the smoothness level of a L generalized solution.