Abstract
Estimates are derived for the total error in solving linear algebraic systems, including non-consistent ones, by one- and two-step iterative methods, with input data being approximate. Criteria for terminating iterative processes are constructed providing a given accuracy of the solution.
Similar content being viewed by others
REFERENCES
D. K. Faddeev and V. N. Faddeeva, Computing Methods of Linear Algebra [in Russian], Fizmatgiz, Moscow (1960).
M. A. Krasnosel'skii, G. V. Vainikko, P. P. Zabreiko, Ya. B. Rutnitskii, and V. A. Stetsenko, Approximate Solution of Operator Equations [in Russian], Nauka, Moscow (1969).
A. A. Samarskii, Introduction to the Theory of Difference Schemes [in Russian], Nauka, Moscow (1971).
G. I. Marchuk and Yu. A. Kuznetsov, Iterative Methods and Quadratic Functionals [in Russian], Nauka, Novosibirsk (1972).
G. I. Marchuk, Methods of Computational Mathematics [in Russian], Nauka, Moscow (1977).
A. A. Samarskii and E. S. Nikolaev, Methods of Solution of Mesh Equations [in Russian], Nauka, Moscow (1978).
K. Flatcher, Numerical Methods Based on Galerkin Method [Russian translation], Mir, Moscow (1988).
V. I. Lebedev and S. A. Finogenov, “The order of selecting iterative parameters in the Chebyshev cyclic iterative method,” Zh. Vych. Mat. Mat. Fiz., 11, No. 2, 425-438 (1971).
V. M. Glushkov, I. N. Molchanov, B. N. Brusnikin et al., Software of Mir-1 and Mir-2 Computers. Numerical Methods [in Russian], Vol. 1, Naukova Dumka, Kiev (1976).
E. F. Galba, “Iterative methods for calculation of the weighted normal pseudo-solution with degenerate weights,” Zh. Vych. Mat. Mat. Fiz., 39, No. 6, 886-289 (1999).
E. F. Galba, “Iterative methods to compute weighted normal pseudosolutions with positive definite weights,” Kibern. Sist. Analiz, No. 2, 105-115 (1998).
A. N. Khimich and M. F. Yakovlev, “Solution of SLAE with semi-definite symmetric positive matrices,” in: Computer Mathematics. Optimization of Calculations [in Russian], Vol. 1, V. M. Glushkov Institute of Cybernetics, Sci. Council on Cybernetics (2001), pp. 392-396.
I. N. Molchanov and M. F. Yakovlev, “Iterative processes of solution of a class of incompatible systems of linear algebraic equations,” Zh. Vych. Mat. Mat. Fiz., 15, No. 3, 547-558 (1975).
Ch. Lawson and P. Henson, Numerical Solution of Problems of the Least-Squares Method [Russian translation], Nauka, Moscow (1986).
A. N. Khimich, “Perturbation bounds for the least-squares problem,” Kibern. Sist. Analiz, No. 3, 142-145 (1996).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Khimich, A.N., Yakovlev, M.F. The Total Error in Calculating Linear Mathematical Models by Iterative Methods. Cybernetics and Systems Analysis 38, 749–758 (2002). https://doi.org/10.1023/A:1021895010938
Issue Date:
DOI: https://doi.org/10.1023/A:1021895010938