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In this study, we consider a general time-space system, whose model operatorand observation operator are locally Lipschitz continuous, over a finite timehorizon and parameter identification by using Landweber-Kaczmarzregularization. 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 severalsubintervals leads to the idea of applying the Kaczmarz method. A lopingstrategy is incorporated into the method to yield the loping Landweber-Kaczmarziteration.

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