中文摘要：

给出了求解一类加权线性最小二乘问题的预处理迭代方法,也就是预处理的广义加速超松弛方法（GAOR）,得到了一些收敛和比较结果.比较结果表明当原来的迭代方法收敛时,预处理迭代方法会比原来的方法具有更好的收敛率.而且,通过数值算例也验证了新预处理迭代方法的有效性.

英文摘要：

The preconditioned iterative methods for solving linear systems based on a class of weighted linear least square problems were proposed,which were the preconditioned generalized accelerated overrelaxation（GAOR） methods.Some convergence and comparison results were obtained.The comparison results show that the convergence rate of the preconditioned iterative methods is indeed better than the rate of the original methods,whenever the original methods are convergent.Furthermore,effectiveness of the new preconditioned methods is shown by numerical experiment.