On the Choice of the Tikhonov Regularization Parameter and the Discretization Level: A Discrepancy-Based Strategy

2014/10/23 by Vinicius Albani, Albani, Vinicius, Adriano De Cezaro +3
Decision Sciences · Mathematics · #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Probabilistic and Robust Engineering Design #Statistical and numerical algorithms

paper · pdf · doi:10.48550/arxiv.1410.6222

openalex publication_date 2014/10/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We address the classical issue of appropriate choice of the regularization and discretization level for the Tikhonov regularization of an inverse problem with imperfectly measured data. We focus on the fact that the proper choice of the discretization level in the domain together with the regularization parameter is a key feature in adequate regularization. We propose a discrepancy-based choice for these quantities by applying a relaxed version of Morozov's discrepancy principle. Indeed, we prove the existence of the discretization level and the regularization parameter satisfying such discrepancy. We also prove associated regularizing properties concerning the Tikhonov minimizers.

Citations

• Numerical optimization

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