Three-parameter Regularization Algorithm for Pseudo-solution of Non-compatible Systems

The work is devoted to some generalization of the regularization method for ill-conditioned and degenerate systems of linear algebraic equations with symmetric non-negative definite matrices. For regularization, a shift of matrix is used with the unit operator multiplied by a small positive parameter. In previous paper of authors, two variants of linear combinations of regularized solutions with different parameters are considered: for consistent and for inconsistent systems. In the first case, the choice of weights for a linear combination increases order of accuracy in comparison with the one-parameter regularization. In the second case, a special choice of weights allows one to find an approximate normal pseudo-solution without orthogonalization of the right-hand side to the matrix kernel. In present paper we combine both approach by usage of three-parameter linear combination to suppress a contribution of operator kernel and to increase order of accuracy for normal pseudo-solution. A computational experiment illustrates the theoretical result.