A necessary and sufficient criterion to guarantee feasibility of the interval Gaussian algorithm for a class of matrices

Günter Mayer; Lars Pieper

Applications of Mathematics (1993)

  • Volume: 38, Issue: 3, page 205-220
  • ISSN: 0862-7940

Abstract

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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 × n interval matrix [ A ] the comparison matrix [ A ] 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.

How to cite

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Mayer, Günter, and Pieper, Lars. "A necessary and sufficient criterion to guarantee feasibility of the interval Gaussian algorithm for a class of matrices." Applications of Mathematics 38.3 (1993): 205-220. <http://eudml.org/doc/15747>.

@article{Mayer1993,
abstract = {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.},
author = {Mayer, Günter, Pieper, Lars},
journal = {Applications of Mathematics},
keywords = {linear interval equations; Gaussian algorithm; interval Gaussian algorithm; linear systems of equations; criteria of feasibility; interval analysis; interval analysis; linear equations; interval Gaussian algorithm},
language = {eng},
number = {3},
pages = {205-220},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A necessary and sufficient criterion to guarantee feasibility of the interval Gaussian algorithm for a class of matrices},
url = {http://eudml.org/doc/15747},
volume = {38},
year = {1993},
}

TY - JOUR
AU - Mayer, Günter
AU - Pieper, Lars
TI - A necessary and sufficient criterion to guarantee feasibility of the interval Gaussian algorithm for a class of matrices
JO - Applications of Mathematics
PY - 1993
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 38
IS - 3
SP - 205
EP - 220
AB - 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.
LA - eng
KW - linear interval equations; Gaussian algorithm; interval Gaussian algorithm; linear systems of equations; criteria of feasibility; interval analysis; interval analysis; linear equations; interval Gaussian algorithm
UR - http://eudml.org/doc/15747
ER -

References

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  1. G. Alefeld, Über die Durchführbarkeit des Gaußschen Algorithmus bei Gleichungen mit Intervallen als Koeffizienten, Computing Suppl. 1 (1977), 15-19. (1977) Zbl0361.65017
  2. G. Alefeld, J. Herzberger, Introduction to Interval Computations, Academic Press, New York, 1983. (1983) Zbl0552.65041MR0733988
  3. H. Bauch K.-U. Jahn D. Oelschlägel H. Süsse, V. Wiebigke, Intervallmathematik, BSB B.G. Teubner Verlagsgesellschaft, 1987. (1987) MR0927085
  4. A. Berman, R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, Academic Press, New York, 1979. (1979) Zbl0484.15016MR0544666
  5. A. Frommer, G. Mayer, A new criterion to guarantee the feasibility of the interval Gaussian algorithm, SIAM J. Matrix Anal. Appl., in press. Zbl0777.65012
  6. R. Klatte U. Kulisch M. Neaga D. Ratz, Ch. Ullrich, PASCAL-XSC, Sprachbeschreibung mit Beispielen, Springer, Berlin, 1991. (1991) 
  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. (1991) MR1189151
  8. R.E. Moore, Interval Analysis, Prentice Hall, Englewood Cliffs, N.J., 1966. (1966) Zbl0176.13301MR0231516
  9. A. Neumaier, 10.1016/0024-3795(84)90217-9, Linear Algebra Appl. 58 (1984), 273-325. (1984) Zbl0558.65019MR0739292DOI10.1016/0024-3795(84)90217-9
  10. A. Neumaier, Interval Methods for Systems of Equations, Cambridge University Press, Cambridge, 1990. (1990) Zbl0715.65030MR1100928
  11. K. Reichmann, 10.1007/BF02265315, Computing 22 (1979), 355-361. (1979) Zbl0423.65018MR0620062DOI10.1007/BF02265315
  12. R. S. Varga, Matrix Iterative Analysis, Prentice-Hall, Englewood Cliffs, N.J., 1963. (1963) Zbl0133.08602MR0158502

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