We show that Nesterov acceleration is an optimal-order iterative regularization method for linear ill-posed problems provided that a parameter is chosen accordingly to the smoothness of the solution. This result is proven both for an a priori stopping rule and for the discrepancy principle. The essential tool to obtain this result is a representation of the residual polynomials via Gegenbauer polynomials.

翻译：我们显示,Nesterov加速是线性问题的最佳序列迭代正规化方法,前提是根据解决办法的顺利性选择一个参数。这一结果既为先验停止规则所证明,也为差异原则所证明。获得这一结果的基本工具是通过Gegenbauer多边协议代表残余多面体。