中文摘要：

迭代极小残差方法是求解大型线性方程组的常用方法，通常用残差范数控制迭代过程．但对于不适定问题，即使残差范数下降，误差范数未必下降．对大型离散不适定问题，组合广义最小误差（GMERR）方法和截断奇异值分解（TSVD）正则化方法，并利用广义交叉校验准则（GCV）确定正则化参数，提出了求解大型不适定问题的正则化GMERR方法．数值结果表明，正则化GMERR方法优于正则化GMRES方法．

英文摘要：

The iterative minimum-residual methods for solving large-scale linear systems are usu- ally controlled by the norm of the residual. However, the errors do not necessarily decreasewhile the residuals decrease for ill-posed problems. Combining the generalized minimal error （GMERR） method with the truncated singular value decomposition （TSVD） regularization, and using the generalized cross validation （GCV） for determining the regularization param- eter, we present the regularizing GMERR method for solving discrete ill-posed problem. Numerical results show that the regularizing GMERR method is superior to the regularizing GMRES method.