Optimal-order convergence of Nesterov acceleration for linear ill-posed problems

01/20/2021

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by   Stefan Kindermann, et al.

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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.