中文摘要：

本文先把正则化后的第二类积分方程分解为等价的一对不含积分算子K＊K、仅含积分算子K以及K＊的方程组，再用截断投影方法离散方程组，采用多层迭代算法求解截断后的等价方程组，并给出了后验参数的选择方法，确保近似解达到最优．与传统全投影方法相比，减少了积分计算的维数，保持了最优收敛率．最后，算例说明了算法的有效性．

英文摘要：

We first reformulate the regularized integral equations of the second kind as an equiv- alent system of integral equations which do not involve the composition integral operator K＊K, containing only the integral operator K and K＊, and then apply the truncated projec- tion method to discrete equivalent system of integral equations, apply multi-level iterative algorithm for solving the equivalent integrM equations, and given the choice of the a poste- riori parameter methods to ensure the optimal approximate solution. Compared with the traditionM full-projection method, we keep the optimM convergence rate, but less than the number of inner products calculation dimension. Finally, numerical experiments are given to illustrate the efficiency of the method,