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# Article

 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: http://hdl.handle.net/10338.dmlcz/103635 . Reference:  G. E. Forsythe С. В. Moler: Computer Solution of Linear Algebraic Systems.Prentice Hall, Englewood Clifs, New Jersey 1967. MR 0219223 Reference:  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:  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:  J. Cifka: The method of the best determined terms.to appear. Reference:  J. Hekela: Inverse pomocí metody nejlépe určených termů.to appear in Bull. Astr. Inst. ČSAV. Reference:  T. L. Bouillon P. L. Odell: Generalised Inverse Matrices.John Wiley and Sons, London, 1971. .

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