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- W4385436657 abstract "The Bregman-Kaczmarz method is an iterative method which can solve strongly convex problems with linear constraints and uses only one or a selected number of rows of the system matrix in each iteration, thereby making it amenable for large-scale systems. To speed up convergence, we investigate acceleration by heavy ball momentum in the so-called dual update. Heavy ball acceleration of the Kaczmarz method with constant parameters has turned out to be difficult to analyze, in particular no accelerated convergence for the L2-error of the iterates has been proven to the best of our knowledge. Here we propose a way to adaptively choose the momentum parameter by a minimal-error principle similar to a recently proposed method for the standard randomized Kaczmarz method. The momentum parameter can be chosen to exactly minimize the error in the next iterate or to minimize a relaxed version of the minimal error principle. The former choice leads to a theoretically optimal step while the latter is cheaper to compute. We prove improved convergence results compared to the non-accelerated method. Numerical experiments show that the proposed methods can accelerate convergence in practice, also for matrices which arise from applications such as computational tomography." @default.
- W4385436657 created "2023-08-01" @default.
- W4385436657 creator A5002877195 @default.
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- W4385436657 date "2023-07-28" @default.
- W4385436657 modified "2023-10-16" @default.
- W4385436657 title "Minimal error momentum Bregman-Kaczmarz" @default.
- W4385436657 doi "https://doi.org/10.48550/arxiv.2307.15435" @default.
- W4385436657 hasPublicationYear "2023" @default.
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