Optimal-order convergence of Nesterov acceleration for linear ill-posed problems
| Autor: | Stefan Kindermann |
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| Rok vydání: | 2021 |
| Předmět: |
Well-posed problem
Smoothness (probability theory) Gegenbauer polynomials Applied Mathematics Acceleration (differential geometry) Numerical Analysis (math.NA) Residual Regularization (mathematics) Computer Science Applications Theoretical Computer Science Signal Processing Convergence (routing) FOS: Mathematics Applied mathematics Mathematics - Numerical Analysis Representation (mathematics) Mathematical Physics Mathematics |
| DOI: | 10.48550/arxiv.2101.08168 |
| Popis: | 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 Hölder 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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