用正则化Symmlq方法求解Symm积分方程

摘要

Symm积分方程是Hadamard意义下的不适定问题.离散该方程将产生线性离散不适定系统.文中提出基于GCV准则的正则化Symmlq方法数值求解Symm积分方程.与Tikhonov正则化相比,在数据出现噪声的情况下,该方法能快速有效地反演出Symm积分方程的数值解.%The Symm integral equation is typically ill-posed in the sense of Hadamard. The discretization of such equation gives rise to linear ill-posed problems. Based on the CCV criterion, a regularized Symmlq method is presented to reconstruct the solution of linear ill-posed problems. Compared with the Tikhonov regularization, the new method can reconstruct the solution of the Symm integral equation quickly and efficiently in the presence of noise corrupted data.