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arXiv · 2101.08168

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

Stefan Kindermann
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Abstract

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.

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Stefan Kindermann. 2021-01-20. Optimal-order convergence of Nesterov acceleration for linear ill-posed problems. https://doi.org/10.1088/1361-6420%2Fabf5bc

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