| 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:
|
[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 terms.to 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. |
| . |
