Randomized regularized extended Kaczmarz algorithms for tensor recovery
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Randomized regularized Kaczmarz algorithms have recently been proposed to solve tensor recovery models with consistent linear measurements. In this work, we propose a novel algorithm based on the randomized extended Kaczmarz algorithm (which converges linearly in expectation to the unique minimum norm least squares solution of a linear system) for tensor recovery models with inconsistent linear measurements. We prove the linear convergence in expectation of our algorithm. Numerical experiments on a tensor least squares problem and a sparse tensor recovery problem are given to illustrate the theoretical results.
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