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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 $j\geq k$.
[1] G. E. Forsythe С. В. Moler: Computer Solution of Linear Algebraic Systems. Prentice Hall, Englewood Clifs, New Jersey 1967. MR 0219223
[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. DOI 10.1137/0708058 | MR 0293867 | Zbl 0199.50803
[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. DOI 10.1137/0710025 | MR 0334486 | Zbl 0261.65034
[4] J. Cifka: The method of the best determined terms. to appear.
[5] J. Hekela: Inverse pomocí metody nejlépe určených termů. to appear in Bull. Astr. Inst. ČSAV.
[6] T. L. Bouillon P. L. Odell: Generalised Inverse Matrices. John Wiley and Sons, London, 1971.
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