Converse results, saturation and quasi-optimality for Lavrentiev\n regularization of accretive problems

2016/07/17 by Robert Plato, Plato, Robert
Computer Science · Mathematics · #65J10 #65J20 #Advanced Mathematical Modeling in Engineering #Differential Equations and Boundary Problems #FOS: Mathematics #Holomorphic and Operator Theory #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.1607.04879

openalex publication_date 2016/07/17 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

This paper deals with Lavrentiev regularization for solving linear ill-posed\nproblems, mostly with respect to accretive operators on Hilbert spaces. We\npresent converse and saturation results which are an important part in\nregularization theory. As a byproduct we obtain a new result on the\nquasi-optimality of a posteriori parameter choices. Results in this paper are\nformulated in Banach spaces whenever possible.\n

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