求解Lavrentiev迭代方程的多尺度快速配置算法

考虑了第一类Fredholm积分方程的求解.采用有矩阵压缩策略的多尺度配置方法来离散Lavrentiev迭代方程,在积分算子是弱扇形紧算子时,给出近似解的先验误差估计,并给出了改进的后验参数的选择方法,得到了近似解的收敛率.最后,举例说明算法的有效性.

Fast Multiscale Collocation Methods for Solving Iterated Lavrentiev Equations

The authors consider ill-posed Fredholm integral equations of the first kind. The authors apply a multiscale collocation method with a matrix compression strategy to discretize the iterated Lavrentiev equation and then analyze the priori convergence of the multiscale collocation method, if the integral operator is the weakly sectorial operator. The convergence rates of the iterated Lavrentiev regularization are achieved by using a modified a posteriori parameter choice strategy. Finally, numerical examples are given to illustrate the efficiency of the method.