Adaptively sketched Bregman projection methods for linear systems

Abstract The sketch-and-project, as a general archetypal algorithm for solving linear systems, unifies variety of randomized iterative methods such the Kaczmarz and coordinate descent. However, since it aims to find least-norm solution from system, sparse can not be included. This motivates us propose more framework, called sketched Bregman projection (SBP) method, in which we are able solutions with certain structures systems. To generalize concept adaptive sampling SBP show how progress, measured by distance, single step depends directly on loss function. Theoretically, provide detailed global convergence results method different rules. At last, (sparse) methods, group numerical simulations tested, verify that utilizing Kaczmarz–Motzkin rule demands fewest computational costs achieve given error bound comparing corresponding other