Abstract
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.
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Funding
This work was supported by the Krasnoyarsk Mathematical Center, funded by the Ministry of Education and Science of the Russian Federation as part of activities for the creation and development of regional scientific and educational mathematics centers (Agreement 075-02-2023-912).
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Shaydurov, V., Petrakova, V. Three-parameter Regularization Algorithm for Pseudo-solution of Non-compatible Systems. Lobachevskii J Math 45, 328–335 (2024). https://doi.org/10.1134/S1995080224010487
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DOI: https://doi.org/10.1134/S1995080224010487