On the Numerical Solution of System of Linear Algebraic Equations with Positive Definite Symmetric Ill-Posed Matrices

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Abstract: In this paper, we present the results of a numerical solution to ill-posed systems of linear algebraic equations (SLAEs) with positive definite symmetric matrices by a regularization method. In the paper it is shown that for the regularization of a computational process by the Tikhonov method it is sufficient to replace matrix A_nof the system by matrix A_n+αE_n where E_n is the unit matrix, and α is some positive numbers (the regularization parameters) that tend to zero.

WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 17, 2018, Art. #3

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I. G. Burova, M. A. Kalnitskaia, A. V. Malevich, "On the Numerical Solution of System of Linear Algebraic Equations with Positive Definite Symmetric Ill-Posed Matrices," WSEAS Transactions on Mathematics, vol. 17, pp. 13-19, 2018, DOI:
I. G. Burova, M. A. Kalnitskaia, A. V. Malevich. On the Numerical Solution of System of Linear Algebraic Equations with Positive Definite Symmetric Ill-Posed Matrices. WSEAS Transactions on Mathematics. 2018;17:13-19.
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