Landweber-Kaczmarz for parameter identification in time-dependent inverse problems: All-at-once versus Reduced version

Abstract

In this study, we consider a general time-space system, whose model operator and observation operator are locally Lipschitz continuous, over a finite time horizon and parameter identification by using Landweber-Kaczmarz regularization. The problem is investigated in two different modeling settings: An All-at-once and a Reduced version, together with two observation scenarios: continuous and discrete observations. Segmenting the time line into several subintervals leads to the idea of applying the Kaczmarz method. A loping strategy is incorporated into the method to yield the loping Landweber-Kaczmarz iteration.

arXiv comment30 pages, 4 figures, accepted manuscript by Inverse Problem (DOI: 10.1088/1361-6420/aaf9ba)

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