Geodesic
Some limit properties of the best determined terms method
Applications of Mathematics, Tome 21 (1976) no. 3, pp. 161-167
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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 $j\geq k$.
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 $j\geq k$.
DOI : 10.21136/AM.1976.103635
Classification : 45B05, 45L05, 65R05, 65R20 
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Neuberg, Jiří. Some limit properties of the best determined terms method. Applications of Mathematics, Tome 21 (1976) no. 3, pp. 161-167. doi: 10.21136/AM.1976.103635

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