Convergence rates of nonlinear inverse problems in Banach spaces: conditional stability and weaker norms

2018/05/30 by Gaurav Mittal, Mittal, Gaurav, Ankik Kumar Giri +1
Engineering · Mathematics · #47A52 #47J06 #47J20 #65J20 #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Photoacoustic and Ultrasonic Imaging #Sparse and Compressive Sensing Techniques

paper · pdf · doi:10.48550/arxiv.1805.11854

openalex publication_date 2018/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this short note, we formulate the convergence rates of the well known Tikhonov regularization scheme for solving the nonlinear ill-posed problems in Banach spaces. For deriving the convergence rates, we employ the novel smoothness concept of conditional stability estimates in terms of weaker norms. Moreover, we show that our results are applicable on two ill-posed inverse problems.

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