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the data matrix large scale linear systems generally have correlated columns and high condition number finding unknows from measurements by using a least-square technique result in noise enhancement. for this reason, robust solution techniques are needed .in this article, we investigate how to regularize the momentum-alterative hessian sketch solver for solving ill-posed linear systems including large-scale data matrices. instead of using a single regularization parameter for all iterations, the proposed solver automatically finds a separate parameter in each iteration without requiring any other parameter tuning and then adjusts momentum parameters accordingly