Solution of a system of linear equations with given error sets for coefficients
Applications of Mathematics, Tome 27 (1982) no. 5, pp. 319-325
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
DOI : 10.21136/AM.1982.103979
Classification : 65F05, 65F30, 65G30
Keywords: interval coefficients; interval arithmetic; two-sided bounds
@article{10_21136_AM_1982_103979,
     author = {\v{S}ik, Franti\v{s}ek},
     title = {Solution of a system of linear equations with given error sets for coefficients},
     journal = {Applications of Mathematics},
     pages = {319--325},
     year = {1982},
     volume = {27},
     number = {5},
     doi = {10.21136/AM.1982.103979},
     mrnumber = {0674978},
     zbl = {0503.65014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1982.103979/}
}
TY  - JOUR
AU  - Šik, František
TI  - Solution of a system of linear equations with given error sets for coefficients
JO  - Applications of Mathematics
PY  - 1982
SP  - 319
EP  - 325
VL  - 27
IS  - 5
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.1982.103979/
DO  - 10.21136/AM.1982.103979
LA  - en
ID  - 10_21136_AM_1982_103979
ER  - 
%0 Journal Article
%A Šik, František
%T Solution of a system of linear equations with given error sets for coefficients
%J Applications of Mathematics
%D 1982
%P 319-325
%V 27
%N 5
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.1982.103979/
%R 10.21136/AM.1982.103979
%G en
%F 10_21136_AM_1982_103979
Šik, František. Solution of a system of linear equations with given error sets for coefficients. Applications of Mathematics, Tome 27 (1982) no. 5, pp. 319-325. doi: 10.21136/AM.1982.103979

[1] M. Balinski: An algorithm for finding all vertices of a convex polyhedral set. SIAM Journal, 9 (1) (1961), 72-88. | MR

[2] R. T. Rockafellar: Convex analysis. Princeton, 1970. (Russian translation Moskva, 1973.) | MR | Zbl

[3] F. Šik: A linear problem of the interval calculus. Ekonom.-matem. obzor, 16 (1980), 37-46. | MR

[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. | DOI | MR

[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

[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. | MR | Zbl

[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. | DOI | MR

Cité par Sources :