UDC 519.2, 519.61, 519.71
1 Space Research Institute of the National Academy
of Sciences of Ukraine and State Space Agency of Ukraine, Kyiv, Ukraine
 v.f.gubarev@gmail.com
|
2 Institute for Applied System Analysis of National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute,” Kyiv, Ukraine
vamdemonsteeve@gmail.com
|
SOLUTION ESTIMATION OF OVERDETERMINED SLAE WITH NONACCURATE RIGHT SIDE
Abstract. Methods of overdetermined SLAE solving when main matrix is precise and right side contains errors
are considered and studied in the paper. It is assumed that each error of right side component is random but being bounded
small interval. Under precise right side system has unique solution. The base of the developed approach is guarantee estimation
of interval membership of the precise solution which may be used for quality estimation of the approximate solution.
These guarantee estimation are namely applied for comparison and solution quality estimation of the solving methods
to be considered. Results of numerical simulation make it possible doing methods comparative analysis and formulation
of the recommendations on its practical application.
Keywords: overdetermined SLAE, estimation, guarantee interval, SVD, bounded errors, LSM, conditionality.
FULL TEXT
REFERENCES
- Voevodin V.V. Computational foundations of linear algebra [in Russian]. Moscow: Nauka, 1977. 304 p.
- Khimich A.N. Perturbation estimates for solving the least squares problem. Kibernetika i sistemnyj analiz. 1996. N 3. P. 142–145.
- Nikolaevskaya E.A., Khimich A.N. Error estimate for weighted normal pseudosolution with positive definite weights. Zh. vychisl. matem. i matem. fiz. 2009. Vol. 49, N 3. P. 422–430.
- Kirichenko N.F. Analytical representation of perturbations of pseudoinverse matrices. Kibernetika i sistemnyj analiz. 1997. N 2. P. 98–107.
- Kudrinsky V.Yu., Truten V.E. Coordination of errors in solving systems of linear algebraic equations on a computer. Zh. vychisl. matem. i matem. fiz. 1982. N 1. P. 223–227.
- Kuntsevich V.M. Control under uncertainty: guaranteed results in control and identification problems [in Russian]. Kiev: Nauk. dumka, 2006. 264 p.
- Golub G., Van Loan Ch. Matrix calculations [Russian translation]. Moscow: Mir, 1999. 548 p.
- Gubarev V.F., Melnichuk S.V. Guaranteed state estimation algorithms for linear systems in the presence of bounded noise. Problemy upravleniya i informatiki. 2015. N 2. P. 26–34.
- Tikhonov A.N., Arsenin V.Ya. Methods for solving ill-posed problems [in Russian]. Moscow: Nauka, 1979. 285 p.
