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Title: Some limit properties of the best determined terms method (English)
Author: Neuberg, Jiří
Language: English
Journal: Aplikace matematiky
ISSN: 0373-6725
Volume: 21
Issue: 3
Year: 1976
Pages: 161-167
Summary lang: English
Summary lang: Czech
Summary lang: Russian
Category: math
Summary: The properties of the criterion of choice are discussed for the best determined termis method (BDT method). The solution of the problem $Kx=y+\epsilon$, where $K$ is $m\times n$ matrix (ill-conditioned), $x\in R^n, y, \epsilon \in R^m, \sum^m_{i=1} \epsilon^2_i\leq \Delta^2$ and $\Delta <0$ given constant, is rather difficult. The criterion of choice from the set of the vectors $x^{(1)},\ldots, x^{(min(m,n))}$, determined by the BDT method, defines the approximation of the normal solution ok $Kx=y$. This approximation x^{(k)}$ should obey the following properties: $\left\|Kx^{(k)}-(y+\epsilon)\right\|^2\leq \Delta^2$, (ii) if $\left\|Kx^{(j)}-(y+\epsilon)\right\|^2\leq \Delta^2$ the $j\geq k$. ()
MSC: 45B05
MSC: 45L05
MSC: 65R05
MSC: 65R20
idZBL: Zbl 0356.45001
idMR: MR0403272
DOI: 10.21136/AM.1976.103635
Date available: 2008-05-20T18:04:32Z
Last updated: 2020-07-28
Stable URL:
Reference: [1] G. E. Forsythe С. В. Moler: Computer Solution of Linear Algebraic Systems.Prentice Hall, Englewood Clifs, New Jersey 1967. MR 0219223
Reference: [2] R. J. Hanson: A numerical method for solving Fredholm integral equations of the first kind using singular values.SIAM J. Numer. Anal., Vol. 8 (1970), 616-622. Zbl 0199.50803, MR 0293867, 10.1137/0708058
Reference: [3] J. M. Varah: On the numerical solution of ill-conditioned linear systems with applications to ill-posed problems.SIAM J. Numer. Anal., Vol. 10 (1973), 257-267. Zbl 0261.65034, MR 0334486, 10.1137/0710025
Reference: [4] J. Cifka: The method of the best determined appear.
Reference: [5] J. Hekela: Inverse pomocí metody nejlépe určených termů.to appear in Bull. Astr. Inst. ČSAV.
Reference: [6] T. L. Bouillon P. L. Odell: Generalised Inverse Matrices.John Wiley and Sons, London, 1971.


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