| Title:
|
A necessary and sufficient criterion to guarantee feasibility of the interval Gaussian algorithm for a class of matrices (English) |
| Author:
|
Mayer, Günter |
| Author:
|
Pieper, Lars |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
38 |
| Issue:
|
3 |
| Year:
|
1993 |
| Pages:
|
205-220 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A necessary and sufficient to guarantee feasibility of the interval Gaussian algorithms for a class of matrices. We apply the interval Gaussian algorithm to an $n \times n$ interval matrix $[A]$ the comparison matrix $\left\langle [A]\right\rangle$ of which is irreducible and diagonally dominant. We derive a new necessary and sufficient criterion for the feasibility of this method extending a recently given sufficient criterion. (English) |
| Keyword:
|
linear interval equations |
| Keyword:
|
Gaussian algorithm |
| Keyword:
|
interval Gaussian algorithm |
| Keyword:
|
linear systems of equations |
| Keyword:
|
criteria of feasibility |
| Keyword:
|
interval analysis |
| MSC:
|
65F05 |
| MSC:
|
65F10 |
| MSC:
|
65G10 |
| MSC:
|
65G30 |
| idZBL:
|
Zbl 0782.65044 |
| idMR:
|
MR1218026 |
| DOI:
|
10.21136/AM.1993.104547 |
| . |
| Date available:
|
2008-05-20T18:45:33Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104547 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] H. Bauch K.-U. Jahn D. Oelschlägel H. Süsse, V. Wiebigke: Intervallmathematik.BSB B.G. Teubner Verlagsgesellschaft, 1987. MR 0927085 |
| Reference:
|
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| Reference:
|
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| Reference:
|
[6] R. Klatte U. Kulisch M. Neaga D. Ratz, Ch. Ullrich: PASCAL-XSC, Sprachbeschreibung mit Beispielen.Springer, Berlin, 1991. |
| Reference:
|
[7] G. Mayer: Old and new aspects of the interval Gaussian algorithm.Computer Arithmetic, Scientific Computation and Mathematical Modelling (E. Kaucher, S.M. Markov, G. Mayer, eds.), IMACS Annals on Computing and Applied Mathematics 12, Baltzer, Basel, 1991, pp. 329-349. MR 1189151 |
| Reference:
|
[8] R.E. Moore: Interval Analysis.Prentice Hall, Englewood Cliffs, N.J., 1966. Zbl 0176.13301, MR 0231516 |
| Reference:
|
[9] A. Neumaier: New techniques for the analysis of linear interval equations.Linear Algebra Appl. 58 (1984), 273-325. Zbl 0558.65019, MR 0739292, 10.1016/0024-3795(84)90217-9 |
| Reference:
|
[10] A. Neumaier: Interval Methods for Systems of Equations.Cambridge University Press, Cambridge, 1990. Zbl 0715.65030, MR 1100928 |
| Reference:
|
[11] K. Reichmann: Abbruch beim Intervall-Gauss-Algorithmus.Computing 22 (1979), 355-361. Zbl 0423.65018, MR 0620062, 10.1007/BF02265315 |
| Reference:
|
[12] R. S. Varga: Matrix Iterative Analysis.Prentice-Hall, Englewood Cliffs, N.J., 1963. Zbl 0133.08602, MR 0158502 |
| . |
