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 under Hlder source conditions. Furthermore, some converse results and logarithmic rates are verified. The essential tool to obtain these results is a representation of the residual polynomials via Gegenbauer polynomials.

中文翻译：

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线性不适定问题的 Nesterov 加速度的最优阶收敛献给 Neubauer 60 岁生日。

我们表明 Nesterov 加速是线性不适定问题的最优阶迭代正则化方法，前提是根据解的平滑度选择参数。这个结果对于先验停止规则和在 Hlder 源条件下的差异原理都得到了证明。此外，还验证了一些相反的结果和对数率。获得这些结果的基本工具是通过 Gegenbauer 多项式表示残差多项式。