| Title:
|
Solution of a system of linear equations with given error sets for coefficients (English) |
| Author:
|
Šik, František |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
27 |
| Issue:
|
5 |
| Year:
|
1982 |
| Pages:
|
319-325 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
In the paper, a method is given for finding all solutions of a system of linear equations with interval coefficients and with additional supposition that these coefficients fulfil a given system of homogeneous linear equations. (English) |
| Keyword:
|
interval coefficients |
| Keyword:
|
interval arithmetic |
| Keyword:
|
two-sided bounds |
| MSC:
|
65F05 |
| MSC:
|
65F30 |
| MSC:
|
65G30 |
| idZBL:
|
Zbl 0503.65014 |
| idMR:
|
MR0674978 |
| DOI:
|
10.21136/AM.1982.103979 |
| . |
| Date available:
|
2008-05-20T18:19:59Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103979 |
| . |
| Reference:
|
[1] M. Balinski: An algorithm for finding all vertices of a convex polyhedral set.SIAM Journal, 9 (1) (1961), 72-88. MR 0142057 |
| Reference:
|
[2] R. T. Rockafellar: Convex analysis.Princeton, 1970. (Russian translation Moskva, 1973.) Zbl 0193.18401, MR 0274683 |
| Reference:
|
[3] F. Šik: A linear problem of the interval calculus.Ekonom.-matem. obzor, 16 (1980), 37-46. MR 0571740 |
| Reference:
|
[4] W. Oettli W. Prager: Compatibility of approximate solution of linear equations with given error bounds for coefficients and right hand sides.Numerische Math., 6 (1964), 405 - 409. MR 0168106, 10.1007/BF01386090 |
| Reference:
|
[5] J. Rohn: Soustavy lineárních rovnic s intervalově zadanými koeficienty.(Systems of linear equations with inexact data). Ekonom.-matem. obzor, 12 (1976), 311 - 315. MR 0448832 |
| Reference:
|
[6] D. J. Hartfiel: Concerning the solution set of $Ax = b$ where $P \leq A \leq Q$ and $p \leq b \leq q$.Numerische Mathem., 35 (1980), 355-359. Zbl 0446.65017, MR 0592162 |
| Reference:
|
[7] T. H. Mathesis S. David Rubin: A survey and comparison of methods for finding all vertices of convex polyhedral sets.Math. Oper. Res. 5 (1980) no. 2, 167-185. MR 0571811, 10.1287/moor.5.2.167 |
| . |
