An approach is proposed to the stable solution of discrete ill-posed problems, based on a combination of random projection of the initial ill-conditioned matrix with ill-defined numerical rank and pseudo-inversion of the resultant matrix. To select the dimension of the projection matrix, we propose to use selection criteria for the model and regularization parameter. The results of experimental studies on the well-known examples of discrete ill-posed problems are given. The solution error is close to the Tikhonov regularization error; however, reducing the matrix dimension due to the projection reduces the computational costs, especially at high noise levels.

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