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.
WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 17, 2018
On the Numerical Solution of System of Linear Algebraic Equations with Positive Definite Symmetric Ill-Posed Matrices
Authors: , ,
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.
Keywords:
Ill-posed systems of linear algebraic equations, Hilbert matrices, regularization parameters
Pages: 13-19 WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 17, 2018, Art. #3 DOI: *As the DOI is a unique identifier, it is already available in the pdf version.
**The DOI link will be activated in the first midst of January 2026.
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